Well someone English suggested England- it’s great here but (I’m English) you asked about cheap, so I’d take it off your list, however good our chocolate is compared to yours, we do not occupy a cheap land!! 😉
I’ll keep my suggestions simple as it sounds like world travel is very new to you and I know most Americans don’t hear much about the rest of the world as your own country is so vast to travel in, plus I’m not too sure what kind of holiday you want- sightseeing/beach/city/adventure etc?
As you have not travelled much, you might be a little nervous. In that case, Europe is quite accessible and not too ‘foreign’. Eastern Europe is by far the cheapest part but please don’t think it’s any less beautiful or historical or that it’s a compromise. Budapest is really affordable and in my opinion as grand and amazing as Paris with its bridges, buildings and castle. And it’s a very young, fun place to be. Krakow in Poland is beautiful too- as is most of Poland. You could get trains between various Eastern European countries and see a lot in a short time. Eastern Europe is also safer in general at night than the big cities of Western Europe which have become a bit seedy in the last decade or so.
I’m also a huge South America fan – Argentina is amazing (plus the male of the species is stunning if you’re looking for that! haha), as is Chile. Both are relatively safe and friendly; the people are just lovely. Lots of incredible natural wonders. If you are feeling more adventurous, Peru has wonderful sights and is cheap- maybe take tours though as you’re a new traveller. Spanish will help in this region but basic Spanish will do, so if you’re in the US you might have learnt enough at school.
If you are young enough to want a party experience and to meet other people, and you’re happy backpacking, you can’t beat Thailand. Even if you’re not, it’s very cheap, easy to get to and would provide a really accessible introduction to Asia, which is dramatically different to anywhere else you’ve been, so will feel exciting and exotic to you, whilst English is commonly spoken and it’s easy to stick to tourist paths if you prefer. Elephants, temples, the best spicy food in the world, beaches- does this sound up your street?
South East Asia in general is a really good bet- it might cost you more in flights than other places but once you get there you’ll get great value on everything else. I think you’ll get a better contrast to USA/Mexico too than if you just go somewhere else in eg. central America. This will help you feel well travelled!
South Africa has fallen on bad times financially so you’ll get incredible value for money on a visit there. Now is the time to visit. Cape Town and safari are two things you could look in to. I would do an organised tour if you’re coming alone, as public transport is not a thing in SA.
Hope that provides some kind of starting point! 🙂 Travelling alone is one of the best things you can do for yourself, so go for it.