Rome has sights all over, many not particularly walkable from each other unless you have a great deal of time in the city. I had 20 days and like to walk a lot, but I still needed to use transit on occasion. Every visitor has his or her own list of sightseeing priorities. The best way to select a convenient hotel for yourself is to start with Google Maps. Enter (one at a time) the names of the places you want to see and click "Save" for each one. You'll end up with a map showing all your hoped-for destinations. Now you can look up your potential hotels and see which one(s) seem best located for you.
I know that Trastevere is a very popular entertainment district with no shortage of restaurants and bars. It's also very atmospheric (if crowded in some areas). Most of the historic sights (the lovely Santa Maria in Trastevere and Santa Cecilia in Trastevere being exceptions) are on the other side of the river. It's easy to walk across a bridge to get to the other side of the Tiber, but it will often be a somewhat longer walk than you'd have from the other three hotels.