I'm planning on heading that way myself later in the year. The current itinerary that i'm working on is as follows:
Charlotte, NC - Carowinds (My first visit) - Highlights - Fury 325, Copperhead Strike, Intimidator
Pigeon Forge, TN - Dollywood (My first visit) - Highlights - Lightning Rod, Wild Eagle, Thunderhead
Orlando, FL - Disney MK, AK, Epcot, HS - Highlights - Expedition Everest (Amazing!) a bit disappointed i'll miss GotG
Orlando, FL - Universal IoA, Studios - Highlights - Hulk (Awesome!), Hagrid's, The Mummy (We got stuck on this last time for a few hours)
Orlando, FL - Seaworld (My first visit) - Highlights - Kracken, Manta, Mako
Tampa, FL - Busch Gardens - Highlights - IRON GWAZI (This will be my entire trip highlight!), Cheetah Hunt, Montu
Winter Haven, FL - Legoland (My first visit) Highlight - Lego
Atlanta, GE - Six Flags Over Georgia (My first visit) - Highlights - Blue Hawk (Apparently is really good now after the refurb), Superman, Twisted Cyclone
I don't drive when in the USA, for personal reasons, so I generally make my way around with Amtrak (Trains) and Greyhound (Buses). It's cheap (Amtrak tickets are as low as $6 one way), but not always at convenient times. For example when I caught the train to Cedar Point it leaves Cleveland at 2am and gets into Sandusky at 4.30am, but only cost me $6.
The 2 tricky parks to get to on my trip using Amtrak/Greyhound are Dollywood and Legoland as neither are really serviced well by public transport (It also looks like the shuttle bus between Legoland and Orlando has been ceased as I can no longer find it on their website). Knoxville is closest to Dollywood and it only looks like a $40 Uber (According to the app) so that may be the way to go there.
All up (assuming there are not closures) I'll visit 12 parks with a total of 73 coasters. Having already been to some of the parks though my coaster count will only go up by about 50. I'll be over there for about 4 weeks and it is actually not costing as much as I thought, at the moment i'm looking at about $7,500 for the lot.
My biggest tip would be to check the parks opening days and times first. I'm planning on a later trip (Sept-Oct) so many of the parks are beginning to wind down for the winter, Six Flags will only be open on weekends, Legoland is closed on Wednesdays, Dollywood closes on Tuesday and Thursdays etc. etc. I would also recommend checking to see which parks are owned by the same company as @colonelbmx said as it is sometimes cheaper to buy a season pass to parks rather than individual tickets, when I did my first USA trip we bought Six Flags ($69.99 for SP vs. $38.00 - $73.00 for a day ticket depending on how you book) and Cedar Fair ($129.00 vs. $49.99 for a day ticket). As we visited a number of parks across both chains and visited for a number of days each we got so much more value buying the season passes.
My biggest Disney tip as a former cast member is:
When you first enter head to the RIGHT and go past Tomorrowland then start making your way around the park in an anticlockwise direction finishing up in Tomorrowland. You tend to find when people first enter Disneyland (Any of them) they tend to head to the left and move around the park clockwise OR head straight to Space Mountain. The best time to hit the biggest attractions (Space Mountain, BTRR, PotC, Splash Mountain) is during parades/fireworks/lightshows.