We've gone to Melbourne a couple of times and stayed at the Radisson that's right on the beach. All rooms overlook the ocean and they are all suites. They even have family suites if your kids are old enough to sleep on bunk beds. The staff there has been absolutely wonderful to us during our stays. Last visit we were there over Thanksgiving and ds age 15 months fell asleep during the whole meal. Our waitress brought over a pillow to tuck behind him so he'd sleep so much more comfortably. When we arrived the next day for breakfast, she was there with the pillow and high chair waiting at a table for us......really went above and beyond. They have a great pool with beach access.
We then went up to Daytona for a few days on another trip and had SOOOOO much fun! We absolutely love the beach there.....easy to walk on and oh so pretty! We stayed at Daytona Beach Resort and Conference Center. Very fancy looking. We stayed in a corner room with views of the city and beach, HUGE balcony, full sized kitchen, bed and living room area (one big open room). Each room is individually owned and decorated and they owners of ours had left some kids beach things to play with. Our son was only 6 months old at the time during this visit, so he wasn't able to enjoy them. They have a kiddy pool and a few other pools that overlook the ocean.
While we LOVED Melbourne, we're thinking of going back to Daytona because of their beach. Soooo easy to walk on. Either way, you'll have a great time on the beach.
Also, check out resorts that are part of timeshares like Interval. They have some resorts that are on the beach, a lot of rooms overlooking the ocean and can get them at very reasonable prices compared with hotel rooms. Would be great for a family.