try Hotel del Corso.
Via del Corso is the main shopping street and becomes a pedestrian street in the evening. It starts in the Piazza del Popollo and is a couple of blocks from Piazza Espana (spanish steps).
I just stayed there for a week and liked it.
paid 120 euros a night for 2. breakfast and all taxes included.
I would not spend the last night closer to the airport.
for 48 euros they will call a car service (on time, clean mercedes-benz, great driver) and it takes 30 minutes to get to the airport in the morning.
I had been to Rome many times but this time I used Frommer's Rome guidebook. He (actually she -his daughter) has some great walks.
I would not stay around Termini. I like to hang out in Termini for the movement and the excitement but not at night. You want to be closer to Piazza espana, Navona, Fontana de Trevi or Campo di Fiori.
Via Veneto used to be the greatest place. it is still nice but tends to be pricey.
The subway is great. only 2 lines but safe, frequent and quick. 1 euro.