My mother lives near the beach and my ILs rent a house there every summer. I've navigated the beach with young babies a few times now.
Bringing a stroller is just a disaster, most of the time, esp. with all the rest of the gear you'll probably want to bring. The wheels are just not designed to roll on sand. It's kind of a nightmare to push, you wind up dragging it, you have to make extra trips for the other stuff.... etc.
I highly recommend some kind of small tent as the previous posters have said. Our current routine includes bringing the tent, which is small and low but big enough for mama to lie inside to nurse the baby if necessary. I pack everything we need into a "beach buggy" - like one of those carts older ladies take to the laundromat

but with big sturdy wheels for rolling on the sand. We take towels, an umbrella, toys, maybe a small cooler. If I want a chair it can be hooked onto the buggy as well, and when the tent is folded and packed in its case the strap loops over the handle of the buggy.
Then the baby goes in a light cotton sling or wrap, and I have my hands free to pull the buggy and even hold on to older DS, if necessary.
I would just recommend, if you get a tent, practice popping it/packing it up a few times at home first. Ours is very tricky and it's a pain to try to figure it out on the windy beach with the sand blowing around, etc.
This is similar to what we have:
http://www.amazon.com/Wonder-Wheeler.../dp/B000M4CVIS
but there are many varieties. Being in a beach town, we were able to find ours locally.