I always stay in Saint-Mère-Église when visiting Normandy (10 trips so far), but I will add a couple of things.
One: You really need a car in Normandy. Yes you could walk the downtown of SME and visit the airborne museum and church, but if you want to visit other related sites (like the Merederet River Crossing, the Utah Beach Museum, the church at Angoville-au-Plain, the causeways and bunkers along the coast, etc.), you need to have a car. This area simply isn't served well, or at all, by pubic transportation.
Two: While there are only a couple of places to eat in town, there aren't nearly so many as in Bayeux. I can only think of two in which I would get dinner that you can walk to from the town center. Nearby Sainte-Marie-du-Mont has another couple, but that is a 10-minute drive.
That being said, Sainte-Mère was definitely the epicenter of U.S. Airborne operation during D-day, and it celebrates it very well. Not only the Airborne Museum, but the Church in the center, the local bars, etc. During anniversaries, this is the town in which the current U.S. Airborne bases itself and parties all night long (do go to The Stop Bar). The aforementioned Merederet River crossing is where the militaries of various countries, along with re-enactors, perform commemorative parachute jumps every year. And on that week, there is a large encampment of re-enactors with their restored vehicles of every type right behind the museum.
I used to stay at a B&B right on the town square overlooking the church yard, but they have changed hands since I started going. I now stay at Valentine 44 B&B about a half block from the town square. The hosts are a wonderful couple that honor and celebrate the "liberation" of Normandy in 1944 (she actually works in the Town Hall and is instrumental in planning the events surrounding the anniversaries). I don't think they have a website, but message me for their contact info if you are interested. Both B&Bs I mentioned are real B&Bs—not "AirBnBs" which are usually really just beds. As far as I know, there is one hotel in town (Hôtel le Sainte Mère) which is on the outskirts, but walkable to the Church square.
Whatever you do, enjoy your visit, and let me know if you would like any additional info. FWIW, I go about every other year on the anniversary of D-day and have parachuted in a few times. Bon Voyage!