Ghana is cheap, safe, friendly, but there isn`t much wildlife compared to East Africa.
[http://www.travelindependent.info/africa-west.htm]
If you can travel in January-February Southeast Asia, New Zealand, India or Central America are all great options.
New Zealand is not cheap, but from 5000 USD you can travel pretty much anywhere.
Central America is generally cheap, cheapest airfares from USA, great wildlife, but not safe and quite busy.
New Zealand, expensive, most expensive airfare from USA, beautiful nature(but not so many animals), safest, easiest place to travel(English spoken, well developed infrastructure, hostels), it`s very busy in Jan-Feb.
India, cheapest, reasonably safe, easy to travel(English spoken, good infrastructure), beautiful nature and wildlife, also busy. It can be quite a culture shock for a first time traveller: dirty, crowded, polluted, lots of hassle.
Southeast Asia, cheap, safe, nature + wildlife OK, easy to travel, but VERY busy. It`s a very good place to start for a first time traveller.
I don't want crazy busy tourist destinations
In most countries there are a few crazy busy destinations, more destinations simply busy and plenty of great places off the beaten track where are very few tourists.