My wife drug me to this area 4 years ago when we got pregnant with our second kid because I travel a ton and she wanted to be close to family. We settled on living in Satellite Beach, it's not the nicest of the 4 beach communities named above but for me it made the most sense, I live just south of the Pineda causway because it makes it super easy for me to shoot to I95 for interstate travel, and I can get to the Orlando Airport in 45 mins. (True that MLB is a decent airport but you have to connect through ATL or CLT, MCO is direct everywhere).
It's perfect for a young family. I couldn't have lived here in my 20's, but there are a ton of young families and a lot of family focused stuff to do. The beachside schools are all 9-10 rated, there are dozens of public playgrouds, nice libraries and parks, of course the beaches, a nice zoo (my wife gets an annual family pass and takes the kids almost monthly). If you like water sports, there is the river for fishing, water skiing, sailing, kayaking, SUP etc etc.
You get a lot of house for your money, it's probably more expensive than Tallahassee, but much cheaper than many other beach-side communities in Florida. The beach is nearly crime free.
As stated above there are a lot of engineers here, that is the primary middle class job. I live in a middle to upper-middle class neighborhood. There are 32 houses on my street, I'm in the Medical Device business, my direct neighbors are a doctor and a dentist couple, on the other side is a lighting business owner, across the street is a CFO with her M&A husband, there are 2 lawyers, one oil and gas guy, a couple that own 2 local restaurants, a retired military guy who is a college professor now, a couple of other retired couples and every other house are engineers, or engineering consultants. When we do any function with the parents at my kids school, it's about the same 2/3 engineers.
I'll give you the lay of the land a bit. You can't go wrong living beachside, but it's more expensive and you get a tiny yard. Melbourne proper is decent but mixed income with so-so schools, West Melbourne has some nice neighborhoods and you can find nice houses for deals there but you may as well live in Tallahasse, you're never going to the beach. Palm Bay... turn on the show Cops, if you watch Cops re-runs 8/10 episodes were filmed in Palm Bay for some reason. It's a dumpsterfire. Viera is the new area, basically they drained a swamp and converted cattle land and sod farms into a new and bustling community. You can get a really nice house there for not a lot of money and all the schools are brand new, a lot of families and close to the freeway. However, again we looked hard but realized we wouldn't get on the river or the beach as much if it was a big production to load up the kids and have to make a big production out of it. There is something to be said about a 5 minute walk to the beach.
Melbourne is a decent mid-sized to small city, there are plenty of bars and restaurants, a couple of cigar bars, 7 breweries within a short drive, all the normal chain restaurants, lots of golf if that's your thing. I've been a lot happier here than I'd imagined. I'm not going to say it's my dream destination for life, but I think it's probably an upgrade from Tallahassee.
As for Miami, my dad lives there and I've been in and out my whole life (he moved there when I was in HS), you couldn't pay me enough to live there, I"m there at least twice a month on business. One of my best friends who is in the same job role I'm at with another company lives there, we have very equal incomes. He moved the from Colorado at about the same time I did, he rented for 3 years because housing is so expensive, the suburbs there suck and there are only a few pocket neighborhoods that aren't crime ridden rat holes. He ended up in Miami Shores in a 3/2 house for $750k, the place was built in the 1960s and could use some work (it has been upgraded a bit but needs more). That coupled with the fact that no matter where you are in the city you have to send your kids to private school because the schools are terrible.
If you want to come down and take a good look around let me know, we have a guest room and you are more than welcome to stay with us.