Ever been to San Diego? A HI Hostel won't break your budget.
http://sandiegohostels.org/
From Alabama, I say fly out and see the left coast.

Washington, DC. The museums are free, and you could take Amtrak. I usually stay at one of the Crystal City Marriotts, they have cheaper weekend rates and lower taxes than DC proper, and sit on top of a metro station, but I've also stayed here: http://www.kaloramaguesthouse.com. Or you could try Priceline.

A big city is the easiest place to be alone.

History and the Beach no passport from Alabama for me...

elconvento.com or Stellaris hotel betterbidding.com priceline.com saves me a lot in San Juan Puerto Rico cheap flights down on www.spirit.com. bookit.com will have some good packages.

Southwest.com good lajolla.com San Diego packages.

For more budget closer and super nice history in FL
Try Casa Monica in Saint Augustine I can usually save a lot driving wonderful great town beach close and a nice Flager Style Historic Hotel.

Discover the Casa Monica Hotel, a majestic 1888 landmark hotel in historic St. Augustine, Florida. Restored in 1999, this castle-like hotel will transport you to a ...

www.casamonica.com

No beach but what about Santa Fe? The weather can be cold still in April but if that doesn't put you off it may be of interest. You can rent a car for a day or two and go out and explore the area too. Very different to Alabama.

Or around Phoenix or Sedona. There are some lovely resorts, so you can be waited on, it will be fairly quiet by April and the weather won't be too hot.

The Oregon coast is another idea. We had warm sunny weather when we were there end of April, and the coast is fantastic. Again hiring a car for a few days means you could explore further.

Hawaii doesn't have to be overly expensive. I can do 10 days for a total budget of $1500 (but I'm in Seattle so my plane ticket is cheaper than yours would be).

I've taken three solo trips to Honolulu/Waikiki. I stay at a budget hotel (~$80/night), walk and take the bus around, go to free and inexpensive activities (Bishop Museum, Iolani Palace, Honolulu Academy of the Arts, farmers market, dance and music concerts outdoors, etc.). $1500 definitely could get you more than only a "few days" if you do some careful planning.

Philadelphia is a wonderful and historic city where you can walk to many of the attractions and use public transportation for even more. There are world-class museums, including the Art Museum with its current special exhibit of Van Gogh. I agree that a big city is great for being alone, and you can do as much or as little as you like. Usually you can get Priceline hotels for under $100 a night, or try the Holiday Inn at 4th and Arch via their website: it's wonderful location for history buffs.

Food is marvelous, and need not be expensive; there are carts and trucks and markets as well as restaurants for every budget and taste.

Here are some April in Philadelphia pictures, just to give you an idea: http://travel.webshots.com/album/334838255hjfcWf

http://travel.webshots.com/album/563154710eoxUAu

And then you can go down to the Jersey Shore for a day or two and watch the ocean from the boardwalk in Ocean City or Atlantic City (depends on if you like casinos; I'm an OC type, myself) or even a couple of days in the very Victorian Cape May.

Hi,
If you are so interested in going to Hawaii then you should go. You can easily manage your expenses if you spend intelligently.
Philadelphia is also a good place to, as you said you are interested in culture, the place has good museums for example and the city is not so expensive.
Have a nice trip!