Pineda Point Marina at the North end, protected, cheap, owners onsite, shared water/power, DIY boat yard, lift, just off the intercostal.
The Pines condos, Indian Harbor Beach/Banana River, pretty well protected, cheap, water/power, no facilities.
Telemar Marina, Indian Harbor Beach/Banana River, protected, pricey, full yard/services/facilities, fuel dock, water/power.
Anchorage Yacht Basin, Indian Harbor Beach/Banana River, protected, $$ unknown (I don't think they're high), full yard/services/facilities, water/power.
And then there are marinas in Crane Creek (South end) and Eau Gallie River (central), don't know them but if you do a search for marinas in Melbourne you can get the contact info.
Palm Bay Marina looks good but there is a short bridge, so no sailboats or large power boats.
There are anchorages on the North sides of Pineda and Eau Gallie Causeways, both completely exposed to East and North.
Do you know the area?
If I can help let me know.