Fiumicino is lovely.
I try to spend a night there either before renting a car (if not going into Rome) or after my trips with a car. (I drop the car off at FCO and take a taxi to the town; reverse the following day in time for flights to USA)
It's a lively place on the water (Tiber canal and sea) with lots of good places to eat.
We stay at the Hotel Seccy; you can walk to the canal and the restaurants. I'm not going to tell you it's the finest hotel, but it's more than okay; they have a variety of rooms in different sizes and for different prices. The cheapest rooms are small. Very nice staff who will book restaurants if you ask. I've also read good things about HOTEL TIBER.
I would not want to stay at one of those big chain hotels in the no-mans'-land between the airport and Fiumicino town, but in Fiumicino itself.
For dinner, there are many options: For pizza and a range of local dishes at low prices, CLEMENTINA.
For a great seafood meal, PASCIUCCI; it's well known as one of the top seafood spots in Lazio; they have tasting menus and also allow you to order a la carte.
You can walk to both from the SECCY.
Here is info, and pics, of our two dinners that last time we stayed in Fiumicino:
https://www.hungryonion.org/t/fiumicino-coastal-town-near-main-roma-airport-two-dinners/36213/2