Are you really sure you want to go to Miami? There are a lot of better beaches than the traffic and crime you will deal with in Miami.
The east coast has waves and more wind. The gulf coast has some nice white sandy beaches, calm seas and less wind. In other words you can enjoy the beach more. The beaches gulf side from around Tarpon Springs down are nice. North of Tarpon Springs you get a lot of oyster beds and not many sandy beaches.
Finding spaces on the spur of the moment is difficult enough in the winter, but finding spaces that will fit a 42 ft rig is going to be a lot more difficult. You will probably need to concentrate on the less popular places, like north of Orlando and into the Panhandle. The further south, the warmer it is, the more expensive it is and the harder to find a site last minute. (and this is last minute) It gets pretty cold in north Florida in the winter.
My definition of the real florida is the springs and rivers in north Central Florida. Rainbow River, Silver River, Weeki Wachee River, Manatee Blue Springs, Blue Springs, Silver Springs, Ichetucknee springs, Ginnie Springs. Basically go on the Fl state parks website and look at the springs and pictures. It's a lovely area and one not to be missed. Getting your rig into many of the state parks will be tricky and they book up 11 months in advance. In fact the most popular places in Fl book for next season before the people leave for the summer. You might get lucky and get a cancellation.
Not in the price range you mentioned, but if you change your mind, we aren't going to be able to get down to our RV lot in the Keys this winter due to my Mom's health issues. We'll be renting it out, but price wise, it's more than you budgeted. Of course the Keys is the BEST place in Florida to winter...which is why we bought a lot. :) BTW, we are in Quail Run Rv resort in Wesley Chapel, plenty of large concrete spots but it's already half full and completely reserved for the winter. You might call and see if there are cancellations, but they usually quit putting people on the cancellation list pretty quickly. Good luck and enjoy Florida.