There are lots of chain hotels in the airport area. Hampton Inn, Comfort Inn, Holiday Inn Express are probably your best bets among the lower priced places.
We've had numerous good stays over the years at both the Hampton Inn on Philbrook Ave and the Holiday Inn Express on Sable Oaks Drive in South Portland. Not sure about the Holiday Inn Express, but the last I knew, the Hampton Inn still offered free airport shuttle service from the hotel to the airport. I'd check with them, because if they can shuttle you to the airport you could return the rental car the night before -- saving at least some time, and, depending on timing, maybe a little money.
try motel6.com / .....exit 48 on 95
The airport is pretty close to downtown so really, just about any hotel is going to be close. If you stay in the heart of the Old Port, that's not going to be cheap. But if you want something different from a chain, check out the Inn at St. John, which has very reasonable rates and is close to downtown. We had a big wedding in June and about half the guests stayed there. Everyone was very positive, said it was clean and comfortable and the owners were friendly. They keep the room rates down because it is 3 stories and doesn't have an elevator but if you can do stairs, it might be an option.