I go quite often to Novi Sad and Belgrade. Cool place, you won't have any problems. The locals, in my experience, are keen to impress. They may ask Americans to please not blow up any bridges while they stay (and then we laugh awkwardly).
Things to know.
They're all tall (seriously, sometimes I think I might get stepped on) and they all smoke (I mean, seriously chaps, at a respiratory medicine conference). They have finally banned smoking in restaurants which seems mostly observed.
Food can be good at decent restaurants, but is never light. Vegetarians are for eating. If you order a veg course expect it to arrive under half a pig swimming in cream. Street food is street food, of course you will die.
The local pivo is called Lav and that's a pretty apt description.
Knowing a few Slavic words (like pivo) will help, though most younger people will be keen to try out their English language skills on you (and their English is generally very good). Cyrillic seems less common in general usage (again amongst the younger population).
I've never noticed any particular surface animosity towards Croats but obviously not a subject to charge into (the company I work with is run by two ex-Serbian army chaps). Hungarian border guards seem universally disliked. There's a casual disregard for all Albanians, Kosovars (don't say it), and Montenegrins as 'lazy'. Generally, there's a fair amount of racism and other isms (not alas uncommon in Slavic regions in my experience).
But I've never had a bad experience. Not even my evening with a badly dressed Albanian gangster.