There is a bus service from Split, Croatia and it can get you to Mostar in about 4 hours. One of the experience that shocked me how casual the immigration process across the border worked. We were told to handover our passports to the guide so that he can get it stamped on our behalf. No one left the bus and were busy doing their own thing. About 15 minutes later, the guide came back with the passports in a plastic bag and started handing it out as if it were some candies. The driver started the engine and left the immigration before everyone got their passport. 

We checked in, dropped our bags and started exploring the city. Quite a few shops selling handmade crafts and lamps. Due to high tourism, shops also accepted euros which made it really easy to transact.  Everything was really cheap - gelato costs around 0.50 euros, cab ride costs us probably 2 euros.