Just curious, but are 100% sold on the whole 4 door thing? What do you use those extra two doors for anyway? Personally, I look for any excuse to not have more than one passenger in my car if I can help it. Those car-less mofos can walk as far as I'm concerned.
Integra's certainly a nice choice, as are the Maxima and Altima. An older Mazda 626 might be nice and would be within your range. Not too sure how fun to drive, but according to Edmunds they get decent gas mileage.
If not for the whole 4 door thing, you could look at a 240SX or an older Sentra SE-R...much higher fun quotient there.