There are no "tropical" diseases in the US which you need to be immunised against. However, in the summer most places will have mosquitoes and other biting insects.
Some areas have more dangerous animals like rattle snakes and bears - though you don't normally get both in the same place!
Dangerous animals will only really be an issue if you are camping in remote areas, and even then deaths or serious injuries are very rare, particularly if you take sensible precautions. Having said that I did once have all my food stolen by a large bear even though it was hanging from 10' above the ground from a tree branch
If you are camping don't drink untreated water even from apparently unpolluted streams, as there is a parasite that has got into most waterways which will give you major stomach problems.
Anyway don't be put off - there is some beautiful unspoilt country to see in the US.