Have you ever heard of Pueblo Ingles? I have done this program in Spain and it is a great experience! You don't need to know Spanish, but your days are spent speaking English with Spaniards who are trying to improve their language skills. All of your meals are provided free, with wine if you like, and your lodging is free. It lasts a week and would let you expand your trip, meet young Spanish professionals and see some of the countryside. I found it in an article in the Dallas Morning News decided it could be fun and have never regretted doing it. We left there with great memories and lots of advice on what to see and do in Spain for the remainder of our trip. It's worth looking into IMO.

http://www.morethanenglish.com/anglos/venue-valdelavilla.asp

I like the idea you have not chosen to move around too much because 7 to 10 days does not go far. The 3 cities you have listed are all very different. Seville is the smallest and you may find that 10 days is too much time without visiting somewhere else for a few days. Both Madrid and BCN have a lot more places of interest within the city boundaries, plus you can take a few days away form them if you like. BCN also has an added attraction of the beach too.
I would suggests you drop Morocco for a day visit, from what others have said you will not be able to see the true country and you are surrounded by a tourist trap. Do a search on here or other forums to read more. Plus it will save on costs!

When are you travelling? This makes a big difference as to what area I'd want to visit.

What are your interests?

I'd second the opinion on dropping Morocco for a daytrip.

Where can I find out info (schedule, rates, etc) about the ferry to Tangier? What are some things I should look out for if I do a day in Tangier? I know I will not be getting a true feel of Morocco if I only spend a day in Tangier, but I would rather do a day in Tangier, then none at all.

We are planning the trip for the last week in June. I would really like to spend some days in a big city, and some days in a smaller countryside town. My friend and I are also big on restaurants and bars and want to make some friends along the way.

Maybe I will drop Morocco...

If you do not drop Morocco (something I suggest too!), take the ferry from Tarifa.
And chances are you'll see only the touristy part of Tanger.

If you choose Madrid, there are some great daytrips: Toledo, Segovia, and El Escorial. I didn't go to the last one, but they are all beautiful. You can easily fill up 7-10 days.

There are a lot of private B&B or hostels with lower prices to help you stay within budget. I'd say plan around 75 euros per night for a double room. I hope you get a good deal on flights.

If I had 10 days and this was my first trip to Spain I'd probably allot about 1/2 of my time in Madrid allowing for daytrips (Toledo, Segovia) then 1/2 of my time in Sevilla with potential time in the white villages, sherry triangle, Cordoba, etc...).

With 10 days (versus 7) you could even squeeze in Granada - just don't try to cram too much into the trip.

It will be warm particularly in Andalucia but I love this area and think a first time traveler to Spain would really enjoy.

Madrid and Sevilla would be easy using public transportation. The high speed train (AVE) only take 2.5 hours - you could probably get some good web fares as long as you start planning your exact dates soon.

"... 1. Fly in/out of Seville, visit Algeciras and day trip on ferry to Morocco (or spend 1 night in Morocco?)"

As far as I know, there is no direct air connection between Boston (or any other US POD) and Sevilla.

I have travelled by MotorCoach Madrid-Sevilla: about half what AVE costs but takes 5.5 hours. I took one departing Estacion Sur de Autobus at midnight.

'...2. Fly in/out of Madrid, basically hang out in Madrid the whole time, stay in or 2 hotels, not venture too far from the city ..."

There are numerous good Hostals in Madrid. From Madrid you can daytrip to Toledo & Segovia using public transportation.

Madrid itself requires 3-4 days to do it justice. Make the midday meal your principal meal of the day (many hostals provide a Continental breakfast). Look for taverns with Menu del dia on a chalkboard outside; wait until about 3:00 PM to eat (most quit serving at 3:30 or 4:00, portions tend to be bigger as quitting time nears).

I vote for Option #2. Skip Tangier! IMHO It's a waste of time.

I think if this is doable or not depends on the price of flights you can get. If you're planning a rip in JUne you're already very late to get flights and have a choice of decent budget hotels. the cheapest airfare seems to be about $700 - leaving you only about $800 for a 7 to 10 day trip. If you want 9 nights in a hotel that will take $450 from each budget - leaving you only $350 - or $40 a day for food, transport and sights. that will mean a lot of walking,, very modest meals (food from supermarkets) and extremely limited nightlife (wine is cheap but other drinks are a fortune and most clubs not cheap to get into).

I would see what you can do to increase your budget - or stick with a 7 day trip. (My 19 year old step-daughter went with some friends for 6 weeks last summer - and she figured about $80 per day for local/intercity transit, meals, sightseeing and evening entertainment - and didn;t come back with a lot of money. And she did hardly any shopping at all.)

The AVE would expenisve for these kids. I think it would be around 150 Euros round trip.