Yakutsk is compact and most of the museums and restaurants in the centre are within walking distance of each other. In summer that is easy and pleasant; in winter it is a serious undertaking — minus 40 air kills exposed skin in minutes, and the recommendation is to walk no further than five minutes between heated buildings.
Bus and marshrutka: A reasonable network of minibuses serves the city for a few roubles per ride. Routes can be hard for non-Russian speakers to navigate; ask your hotel for the right number.
Taxis: Cheap and abundant. Yandex Taxi works in Yakutsk and is by far the easiest option in the cold — you can wait inside until the car arrives.
Walking on the river: From late November to April, the Lena is solid enough to walk and drive across. Stick to the marked routes; thin patches around the city's warm-water outflows do exist.