I had to chime in as this post tickled me. I have had several (4) nursing summer babies so I know what you mean. If it was a pool or a lake, i would either only go in up to my waist and not get my chest wet at all, or if I did swim before we went back to our camper (that is where we swam on vacation) I would wash my nipples off with bottled or fresh from home water. I was just always concerned about the baby picking up some bacteria from the water and it going directly into their mouth. We camp right on a beach of Lake Michigan (a large fresh water lake) so also the combo of a wet bathing suit and sand and having to pull it up to nurse was just too uncomfortable. I also would wash my boobs off if I was staying some place in general because the water wasn't our water or the water we were used to. Maybe overkill but I've had one month olds on camping trips so I wasn't taking any chances. I would take a bottle of water and run it over my nipples. I know that is strange water too but it just made me feel better. If I were swimming in a pool with cholorine, I would definately do this also.
Oh and if you do nurse at a beach, my advice, make sure you have a comfy chair!!!!! After 4 kids you'd think I'd remember to take one with me but I was always leaning up against a beach umbrella nursing, not to comfortable. I'd also always have a large t-shirt to put over my bathing suit so I didn't feel like I was flashing the world pulling up a tight bathing suit.
I also never put sunscreen on a babe that young. under 6 months it's easy to plant them in a place in the shade and have them stay put. We had a small little baby type tent and it still let too much light in so we put towels over the top. Be careful of the water too, even if they are in the shade if my children were facing the water they would still get tons and tons of sun. It was amazing.