There are several bus/marshrutka stations in town. You’ll arrive at the main bus station, which is about 1.5km from the waterfront. From here, trolleybuses 1, 2 and 3 go down the hill along vul Kievskaya to the centre.
Behind the main bus station, on the lower level, you’ll find the buses and marshrutky going to the sights around Yalta. The 27, for example, heads to Alupka (5uah).
Other marshrutky leave from the bus terminal near the central market (eg the 34 to the Nikitsky botanic gardens) or the Spartak Cinema (eg unnumbered marshrutky to Livadia Palace).
There are several metered taxi firms and they’re definitely cheaper for journeys within the city. Avka-Trans Taxis (231 085, 8-067 563 0444) is good, but you can generally find some sort of metered cab at the intersection of vul Ruzvelta and nab Lenina.