Bistriţa was founded in the early 13th century by German settlers and (due to its location on the main trading route with Moldavia) became one of Transylvania's major Medieval cities. Several interesting sites from that time survive in the city's old quarter. Some tourists are also attracted by the fact that the town was mentioned in Bram Stoker's novel Dracula.
Bistriţa is on a secondary railway and gets limited service: a few local trains, three commuter trains from Cluj (a three hours trip) and a night train from Bucharest (nine hours) via Brasov . Timetables can be found on the website of the railway operator CFR 
There are frequent buses from Cluj (two hours travel time), three-four buses from Suceava (four hours and half), Târgu Mureş (three hours) and one bus from Iaşi (seven hours). Some of their schedules are available on autogari.ro .
The relatively compact old quarter can be visited on foot. The rest of the city is covered by several minibus lines operated by Transmixt . At this moment there's no bicycle rental shop in Bistriţa, which could be useful if you like to visit nearby places and you don't have a car available. A good alternative is minibuses or hitch hiking, which is common practice among locals.
The historical centre is hemmed in by more recent building blocks, but is well preserved. It's great for a leisurely walk in summer. You can use a medieval pasaj, that connects the major streets in the centre, to make your own route. These narrow passages are pedestrian only and you can find hidden gems here, like cozy bars and restaurants.
Unfortunately there's little room in the historical centre for outdoor drinking. Only in a small area next the Biserica Evanghelică called Pietonalul on Strada Liviu Rebreanu is reserved for pedestrians. Go for example to Viena Cafe, which has a nice vibe with tasty food and excellent coffee.