I visited Sarajevo and Mostar in the summer of 2004, and I expect my advice, such as it is, may already be out of date, because my Eastern Europe guidebook, published the year before, definitely got a few things wrong, but here goes.
– ATMs are available in both cities (this was one of the things the guidebook got wrong). If you’re staying in private rooms and eating cheaply, as I was, you can figure on spending around 25 Euros (50 convertable marks) a day. “Convertable marks”, by the way, is something of a misnomer; don’t plan on being able to change them back after you leave the country.
– The only options for accomodation in Mostar are hotels (expensive) and rooms in private homes (cheap, I’m not sure the tourist office has set up an official service yet, but there are people at the bus station offering them). In Sarajevo, you can go to an accommodation agency to reserve a private room, and there’s also a hostel in the Turkish quarter, which is a fairly grotty but friendly place. (It claims to offer laundry, but the washing machine was broken while I was there. They do offer a tour of the city in English, which I didn’t take, but which other guests highly recommended.)
– The tap water is fine to drink, as is the water from the public fountain in the Turkish quarter in Sarajevo – where, by the way, you can get the best doner kebabs in Europe, and some really fantastic cakes and pastries.
– The National History Museum in Sarajevo is definitely worth it, at least if they still have the exhibit about the siege. The Gazi Husref-Bey mosque is absolutely gorgeous, at least from the outside (dress code for women is a long skirt and a headscarf, which I didn’t have, so I haven’t seen the inside). If you have any interest in seeing the Archduke Franz Ferdinand’s assassination site, take a good map; it’s unmarked and really hard to spot. In Mostar, there’s a museum called the Turkish House, which is pretty interesting – it’s a restored house from the sixteenth century or thereabouts, and the guide is terrifically knowlegeable and fluent in English. The bridge was still being restored when I was there, but I understand it’s re-opened now, and the city is probably less of a giant construction area than it was – although they still had a great deal of rebuilding to do, so I make no promises on this point.
– The bus service between Mostar and Sarajevo is frequent, and pretty good (it’s a beautiful journey), but schedules change frequently, so double-check when the bus leaves when you buy your ticket. You’ll probably have to dodge a few touts at the bus station in Sarajevo (“Miss, where you going, miss, you want taxi?”) but they’re only a minor annoyance. The city bus schedules are a bit difficult to figure out, unless you’re lucky enough to run into somebody who speaks English, and services such as the left luggage office at the station are understaffed and rather frustrating to use, so leave plenty of time for dealing with this sort of thing.
Anyway, I strongly encourage you to make the trip – it’s a beautiful and fascinating country, although a tremendously sobering place for obvious reasons. (I’m also really glad I had the chance to return the favor after you gave me such great advice on Bulgaria, by the way – I flew out for an interview a couple of weeks ago and had a great time, although I’m still waiting to find out whether I’ve got the job.)