Certainly in Croatia and I imagine in the other places, it is quite common to rent rooms (called sobe) or private apartments--and I dare say they are not much more costly than a hostel.
You did not tell us how many days you have.
On the contrary, I find small towns less expensive, but transportation then becomes an issue. Are you wanting to use public transportation only?

No age limits on hostels. No reason to be nervous. Your mother may not be wild about dorms, I'm certainly not, but many hostels now have private doubles. I agree with yorkshire that sobes are a good option. You should check Lonely Planet or Rough Guide guide books for addresses for agencies handling them. Or, in a lot of place, arriving ferries and buses will be met by locals offering their sobes. You don't mention a budget, but guesthouses and pensions aren't too expensive in Eastern Europe.

I'd suggest that your mother read "Europe Through the Back Door" and possibly "Practical Nomad" for budget traveling tips.

I (older female traveler) recently visited some of the areas you're interested in, by public transport - Belgrade and Sarajevo in particular:
See http://www.fodors.com/community/europe/the-b-trip-part-two-serbia-and-bulgaria.cfm
and http://www.fodors.com/community/europe/the-b-trip-part-three-western-balkans.cfm

Given that you will have some knowledge of Romania, would it not make sense for you to use that knowledge and visit Romania (Maramures, Bucovina, the areas around Sighisoara, Brasov and Sibiu)?

You might want to take a look at my trip report, even if it is getting a little old. Click on my name to find it.

Sounds like a lovely post-graduation trip! And I think it's great that your mother will join you. Being a bit nervous before one's first trip abroad seems quite understandable to me, but I have every reason to believe that if she packs her sense of humor and a willingness to be open to the unexpected, she will have a fabulous time. You'll have to let us know!

I don't see a reference to your time frame, which may be worth considering. If you visit all the places you mention, you will be spending quite a lot of time in transit, so you'll want to be sure that doing so makes sense given the amount of time you'll have in each place.

> Our tentative plans are Cluj to Belgrade to Sarajevo to Zagreb (possibly Zadar) to Ljubljana

I haven't been to Cluj and Belgrade yet, but have been to the other places you mention. I loved Sarajevo, and thought it worth at least 2 or 3 days. Are you considering a stop in Mostar? Also well worth seeing, if a tad bittersweet. I thought a day sufficient for Mostar.

I thoroughly enjoyed close to 3 days in Zagreb, which I believe to be underrated. I should mention, though, that I enjoy spending time in museums; if you don't, a day or so might work better for you.

I also enjoyed a day in Zadar, but it strikes me as a bit off your path. What is it about Zadar that appeals to you?

If you are in this part of the world, do consider a stop in the Plitvice Lakes park - stunning! Well worth the better part of day, and most easily seen if you include a night in the area either before or after exploring the lakes.

Ljubljana is absolutely charming. If you can, I'd encourage you to include time in Lake Bled - say 3 days for the area.

Hope that helps!

I agree with Michael - don't give short shrift to Romania if you're there already and haven't seen the places on his list. Not clear on your plans but you only mentioned moving on from Cluj to other countries. I've been lucky enough to see a few places and Romania was one of the most unique.

I would encourage you to spend several days in Sarajevo which is a fascinating city and not "touristy." I wrote a trip report about our stay there in October 2010 which you can find by clicking on my screen name.

We stayed with a friend and at a hotel which we liked but which is more expensive than what you are looking for.