There are fans of absolutely every location in Paris and even a few of the suburbs. It's just a matter of priorities and budget.

The main obvious thing to keep in mind is that in general, the closer you stay to the center, the more you will pay for everything: accommodations, meals, sundries...

... and the least time on public transportation getting around.

Hi
I've stayed in over 100 hotels in Paris and I've kept track of most of them.
I've started to choose more and more 3 stars over 2 stars - you have less bad surprises - and avoid most 4*, they are basically 3 stars more expensive and with slightly better amenities. Since I don't sleep in those, I just consider it a waste of money - my philosophy.
There are a lot of hotels I could return to but but only about 1/3rd that I would recommend.
Of those, 4 are in the 17, 3 in the 18, 4 in the 11th and 3 in the 4th and 3 in the 6th.
The worst for me is the 19th, can't recommend any hotel there and slept in 6. But usually 19th is my last choice so I figure I end up not in the best !
Best ratio price/qulaity for me has been found in 18th.
About all arr seemed nice to me except 19th, on southwest.
For me location 'close to attractions' is not a must for 3 reasons :
1. as Ker stated : you go once to the site,
2. the metro is gorgeous in Paris
3. sites are spread all over Paris : Sacre Coeur in 18th, Eiffel Tower in what, 8th, Arc de Triomphe elsewhere and catacombs yet at another place... (I lost my map of arrondissement, was quite helpful).
One arr that I avoid is 5th : very touristy, very expensive, lots of 'bof' restaurants. My last experience there was last month, I noted that the hotel was a 'clapier bien aménagé'... 'Clapier' is where you put rabbits. Smaller is illegal I'd guess...

(I thought the Eiffel Tower was in the 7th?)

Five minutes on the Metro? Oh, how I wish THAT were always true.

I do not understand this obsession with time spent on the Metro, and suspect it comes from people who haven't actually spent much time going from one end of Paris to the other using the system, but are basing their ideas on Google, mere supposition or faulty memories.

Trains run on the average every 4 mins throughout the day - so if one is too crowded, it's not such a big deal to wait for the next one. Changing lines only takes 5 minutes - you just have to follow the signs in the corridors. It takes about 30 mins to get "across town" from Republique to Ecole Militaire, about 25 mins to get "all the way" from Montmartre to Hotel de Ville - there are 1440 minutes in a day, so that's not a huge chunk of time.

Anybody with any sense would acquire and study a transport map BEFORE arriving in a foreign city. Easy to do, especially since you can download them for free. Of course, if you wait till you are actually in the station and don't have a clue about how the system works, it is definitely possible to waste a whole lot of those 1440 minutes - but you would only have yourself to blame.