If you want to and it makes sense time wise, Friedrichshafen is better than Meersburg, being connected by train. Still feels a bit like a hustle to me though.
As to the question of cars: Do you plan to book one when there? Numerous providers have offices.
Regardless, I am not sure if Konstanz or any other town works better. You can trip ÜB-KN by train, and most other places are then either connected to both or neither. Proximity matters, of course. Reichenau is closer to KN, Uhldingen closer to ÜB. ÜB is essentially walkable in total - train, spa, shops, lakeside, restaurants.
Regarding the weather, I have to disagree with KCG to some degree. It is cooler, but historically comparably dry - and not yet the time of fog and misery, which comes in November. As noted before, it is still a bit of a lottery: 50F and drizzle are in the cards, but so are 75F and sunshine (chilly when the sun is down though). Prepare for both and hope for the best.