Our trip to Normandy was in October and we stayed in Bayeux for the D Day part of our trip (about 1 1/2 hours from MSM) and Honfleur after that (about an hour in the other direction from Bayeux). Honfleur was lovely as an overnight and you will know why so many people set it as their destination, only you will be there without the crowds. We stayed the Le Cheval Blanc that is on the corner of the harbor, and unlike the complaints we read about noise during the busier tourist season, we found the morning sounds through our open window enjoyable and of local character. Here is what we did on our trip, and maybe you will find something here that works for you:
As others have said, Bayeux is wonderful...it was the first town liberated after the invasion and thus, relatively unscathed during the war. The people are warm and welcoming, and here is a discussion I have particularly enjoyed on this topic:
As another alternative, you might want to think about this B&B, that if I'm not mistaken is on the MSM side of Bayeux vs. the Honfleur. This has been a base for D Day travelers, and staying here might work if you are planning on touring the sites on your own.
The owner can help you with that info!
...just some thoughts and you will know what works for you. As for weather, expect damp mornings and dress in layers. My UGGs kept me warm and dry on the damp fields and beaches in the morning and I wore a coat with a light sweater (maybe, a vest) under it. I shed my coat as the day warmed up, but it didn't warm up too much and the boots did not become too warm for the full day's outing,