It's not whether the hotel is basic or not, it's the location. Not the best, & certainly not a good choice with 3 young chidren.
If you could actually give your budget price per night in euros for all 6 of you (is 2 triples an option?) maybe you will get some better suggestions.
I know all the central hotels, many have triples, a few have quads, so it's not impossible, but budget is key to what is available for you.

Do not stay at this hotel, it is only one block away from Exarchia Square, a square full of drug addicts and a place where the anarchist scene of Athens is based.......
This means that there is a good chance of fights between anarchists and the police, something that i am sure you wouldn't like to experience....
Best places are near Syntagma Square or near the Acropolis.
I don't think that you will find a hotel that will accommodate 5 persons in one room ( Exarchion was rather the exception). It would be nice to know apart from your budget, also the age of the children....

Immediate thoughts,
Arethusa, 2 x triple (through Venere.com)
Attalos, 2 x triple (through LateRooms.com)
Cypria, 1 quad + 1 double (through Venere.com)

Thank you for your advice. I think I will definitely avoid Hotel Exarcion after your comments.
Our budget is around $150 per day although we will do a little more if we have to. The euro-dollar exchange rate makes it a little tough. Now I am thinking of the Marriott Ledra as I noticed it was recommended on this forum. It is more expensive but it seems a safe choice. It also seems to allow 2 kids in a room and perhaps they will be flexible and allow 3 as they are a US chain. They have a summer special going on and the advance purchase non-refundable price may not be too bad. Any thoughts?

Ledra Marriott is an excellent choice, and oceans apart from Exarchion ( 5 stars vs 3 ). It might not be in the top centre of Athens, but you can take the shuttle bus of the hotel, that goes to the center. price is 2 euro per adult, children under 12 years are free. The fee of 2 euros apply from the hotel to the center... The ride from the centre to the hotel is gratis . Infront of the hotel you can also take a local bus , after few stops you can reach easily the Acropolis and Syntagma Square.

Thank you so much! You all are super helpful.
I will try to book Ledra Marriott today and hope it works out.
Yiassas - thank you for the other hotel suggestions.
I will take a look at them if the Marriott does not work out for some reason.

oh and one more thing....
regarding advance purchase -non refundable rate
Any hotel in Greece can be cancelled free of charge up to 21 days before the arrival. Cancellation charges, cannot be applied if cancelled on time, you are entitled to a full refund....
Just for your information, as this kind of offer becomes more and more popular in Greece ( but is against the law, as described above)

Wow, that is really good to know.
All the hotels seem to offer much better deals if you pay the entire amount in advance and they claim it is completely non-refundable.

Thanks!

All the hotels I mentioned are within yards of either Syntagma or Monastiraki metro stations, very central & walkable to everything (most of the major sites are within a very small, mostly pedestrianised area)
Of the 3 the Cypria is the nicest (I have stayed at all 3) & although the Ledra is good there is nothing nicer than being so close to everything, especially with 6 of you, including the children. I would again choose location first, the Ledra is on a very busy road 24/7. I am not against it, if a couple don't mind staying a bit out of the centre that's fine, I'm just thinking that in your situation it may not be so convenient.
I have stayed in more than a dozen central hotels over about 20 visits in the last 2-3 years & I would always advise anyone there to see the sites to go for location first.

Early July is low season in Athens, hotels are dropping their rates, this is why the Ledra Marriott offers an attractive price. Difference between Marriott and the hotels yiassas is suggesting is huge... on the other hand you would be in the middle of Athens if you chose one of these hotels.
You may want to take a look also at : Athens Gate and Parthenon ,both a few meters from the pedestrian walkway of the Acropolis.
Should you book the Marriott make sure that the rate includes also breakfast, non refundable rates usually do not include any breakfast and paying for it on the spot, would be 20 euro per person in a hotel of this class.....

Agree, Athens Gate & Parthenon hotels are also great choices (I've stayed at the Parthenon 5 times). Both the Parthenon & Cypria have really good breakfasts, hot & cold, cereals, fruit etc.

I didn't mention them first as they are more expensive & the bargain rate you can get at the Parthenon (I've paid as little as €69) only applies to doubles I believe.

yiassas you have an excellent knowledge of hotels in Athens, however i would rather exclude Athinas Street and hotels such as Attalos, Baby Grand or Fresh due to the current situation with all the illegal immigrants in the center. During the day there is no problem, but at night i wouldn't feel safe there ( unfortunately) .
Athens Cypria and Arethousa, both have an excellent location near Syntagma Square.

Yes, Attalos would be at the bottom of the list for that reason, although if anyone is staying there I always tell them to turn right as they come out of the hotel in the evenings! At least it's not so far up Athinas as Fresh, I think the Attalos is as far as I would ever recommend. A real shame as there is the new Athens Centre Square hotel, nice place, shame about the location!
My most recent stay (I came back last Thursday) was at the Carolina on Kolokotronis with my 83 yr old mother. We walked back there fine at 1.30am, but if we were coming from Monastiraki direction we walked up Aiolou as far as Agia Irini, then cut through.
Back to the request, all things considered, the fact you need triples or quads, good breakfast, location & price, I think the Cypria would suit, unless you can get a good deal at the Parthenon. Athens Gate is good, but on the main road again & more expensive.

Thanks everyone, I really appreciate your help.
Last night we tried hotwire and ended up booking 5 rooms at the intercontinental for a really good price ($93 per room/day). We did not know it was the intercon until after we accepted the bid but luckily it worked out. The rooms sleep 3 persons each. We have two other families joining us so 5 rooms covers everyone. Breakfast is not included and I'm thinking of emailing them to see if I can pay for it now at a reduced price. I'm so glad I decided to check with you guys before booking Exarchion.

Strikes seem to be heating up in Greece right now.
We are so excited about our trip, I hope things are not too crazy politically when we get there.

You guys have been so helpful, I was wondering if I could ask one more question -

Would it make sense to try to get a personal tour guide for a day in Athens as we are a large group (7 adults + 7 kids)? We have 4 days in Athens and we were thinking the kids might enjoy taking the hydrofoil to Hydra one day. Athens is at the end of our trip and we will be in Crete for 10 days before then.

There are no sigificant strikes in Athens at the moment,and i am not aware of any in the near future ( which means nothing ofcourse as this can change overnight)
The Interconti is a good hotel, located closer to the center as the Ledra Marriott, but still not in the center....
Keep in mind that they usually never give any discount on breakfast....and to get a group rate you should have at least 21 persons.....
A personal tour guide would be an excellent idea, personally i don't like being in a group of 50 people....
During the 4 days in Athens you could also visit Sounion ( with or without guide) to see the temple and a wonderful sunset !!! As for Hydra it would be nicer to go their on your own, and not take the so called 1 day cruise to 3 islands , where you visit theoratically speaking 3 islands , without having enough time to see them...

Any ideas how to find a personal tour guide who is friendly, well-informed, flexible, can take us off the beaten track a little bit.

I agree, I hate large tour groups.

We plan to do hydra on our own, not as part of a tour.

here's the link to a very good and experienced guide.
Ask him to suggest a tour based on what you would like to see.

http://tourguides.viator.com/tour-guide-athanasios-binopoulos-11464.aspx