Looking for suggestions on Charleston and Raleigh

Charleston is FABulous!  Be sure to visit a plantation, Sullivan's Island and Folley Beach if you have a car. Walk the Battery, and take a tour of an historic home in town.  Go to the Straw Market (Historic Charleston City Market), eat at Jestine's Kitchen and The Wreck (Sullivan's Island - S.N.O.B.s, Hominy Grill are great, but spendier. Eat pralines from street vendors, take a buggy ride - soak it all in, and ENJOY!

CHARLESTON is beautiful, but cheap and CHARLESTON are not words used in one sentence, I'm afraid. My recommendation would bento stay in a chain hotel near Summerville or Goose Creek and drive in. There is one hostel on Spring Street, NotSoHostel. Could try that.

The only place I can speak for is Boone plantation ball.  You definitely

want to go there.

Let me talk about Raleigh, since others haven't. The downtown is in a growth spurt, with several close in historic neighborhoods being refurbished by young singles and families. The Glenwood Avenue area is one to check out, very centrally located and close to the many (free) state museums, including the North Carolina Museum of History and the North Carolina Museum of Natural Sciences, both worth a stop. You might also want to check out nearby Durham (North Carolina) where Duke University offers lots of cultural programs, many of them free. Durham is an emerging foodie capital, and has numerous new breweries, cideries and distilleries. Living costs are more reasonable here than in other towns in the area, too. 

Yes you can stay outside the city - Summerville is one possibility or possibly Mount Pleasant (South Carolina)  The CARTA bus system in Charleston is pretty good.  The DASH Trolleys are free.

But there is also a Hampton Inn (free breakfast) right next to the visitors center in Charleston and you can get information and sign up for tours (or not - just decide where you'd like to go on the DASH Trolley).

I have not found that it was hard to eat cheaply in Charleston - you just have to order judiciously.  Here, as elsewhere, we get a big lunch (cheaper) and then take the leftovers back to the hotel for supper. 

Definitely go to Fort Sumter National Monument(you can get the boat from either Charleston or Mt Pleasant), and Fort Moultrie  Also right next the Ft Sumter dock is the South Carolina Aquarium (not especially cheap, but you don't have to pay for the extras like the IMAX). The The Charleston Museum right next to the Visitor's Center is interesting if not especially well curated. Sullivan's Island is interesting, but probably crowded in summer.   Although most sites list Magnolia Plantation as an Audubon swamp site, there is also an Audubon site out at Beidler Forest  When I decided to visit a plantation, the one I visited was Middleton Place  There is also an inexpensive ($3.00) museum and park at Old Santee Canal Park 

I don't have any experience of Raleigh