Keef, them little dogs are the baddest. How tall are you? Look up the Yamaha tw200. It doesn't matter what year you get, they have not changed since 1985 or so. 2001 and up came with electric start. They have big wide tires. Would be great for sand and beaches. It's more stable than a dirt bike with the narrow tires. I rode one for about a year. It's a sweet little bike. Will run flat out at 71 mph. Likes to cruise at 40-50 mph. Gets about 60 mpg. Or better.
I am 6'1 and the bike was little with me.l, but it was not too small. I rode it to work 50 miles a day. I miss it actually. It's not a bike to jump stuff, but it's plenty big enough to ride and have a blast on. Has decant power. You should be able to find one nearby for a good price. Most tw's are sold near a "resort" town. Mine was sold in Daytona beach. If your wanting something a little taller, look at the Honda crf250. Both bikes are 100% street legal. Can handle any dirt road, and will be ok for some light trails.
I ride interstate, and cross creeks on mine. Very versatile. I would sit on both, it's not as good as riding it but it will give you an idea. For what you will be doing, the tw200 won't let you down. And those fat tires will be an asset at the beach.