So I'm from Romania -- living all over the map now, though.
hooligan, I generally eat at family members' houses, so I don't know about restaurants (though I'd be curious) -- where are you going? My hometown is Cluj-Napoca, which is in the northwest in Transylvania. It's a university city, and where there's students, there must be alternative dining to some degree. We've got a slew of immense grocery stores, so at the very least you'll be able to find stuff there. (I'm sure a bigger city you visit elsewhere will have this option too.)
I also suggest, if you're into farmers' markets, to check out the local piata (pronounced piatza, you know, that zz sound in pizza); that's really truly a farmers' market and there should be multiple ones wherever you go every day. It's great to get fresh vegetables/fruits/breads and an even better opportunity to get some local flavor: screaming vendors, big, jolly, toothless ladies.
Otherwise one dish I adore and know is vegan (though some people make it with mayo, then it looks more creamy-white, and it's not half as tasty IMO, my veganism aside, 'cause it steals from the flavor) -- salata de vinete. It's an eggplant spread made from roasted eggplants and some manner of vegetable oil; it's green in color and I could eat it with a spoon.
Watch out for things that're fried or cooked in animal fats, though, and everyone probably spikes the soup with animal even if there's no visible meat. If at a loss and on the spot, go for the garden salad (or the dessert, should be vegetarian). Also, look up the words for foods you want to avoid so that when you're scanning a menu, you're not left clueless.
If you're vegan (okay so you said you're not, but then here's some things you could go for)...
egg/s = ou / oua
cheese = branza (the first "a" has a little hat on it)
milk = lapte
sour cream = smantana (the "a"s are hat-wearers, last one wears his upside down to be cool)
whipped cream = frisca ("s" has a tail, "a" has a hat)
sausage - carnat (first "a" has hat, "t" has a tail to make the tz sound)
beef/veal - vita / vitel ("t" has tail for vitel)
chicken - pui
fish - peste ("s" has a tail for the sh sound)
seafood - fructe de mare
lard - untura ("a" has a hat)
"fasole" is beans, but be warned that there's generally bacon involved
Maybe I'm forgetting something, I'll add if I remember. Let us know how it went, though, and enjoy! There are some stunning stretches of nature, especially near the mountains; so definitely take any opportunity you can to get out of big cities and explore. (Though I'm going to shamelessly plug my city Cluj as something worth seeing, there's some great architecture and museums; Sigisoara is absolutely fabulous too, "Dracula" was born there, either way, a gorgeous fortified city.) Great unexplored spot for a honeymoon -- what made you choose it?