I'm having an overnight in Launceston later this year and have been looking into this very issue of getting to Lauceston city from LST. From experience at LST. Uber can be expensive, due to the tricks they play with surge pricing, etc. Cabs are not far behind either.
So I have come to the conclusion that I will either rent a car from Hertz (as I can get corportate rates), or try the walk/bus option. I have used the local buses in that part of the world before (to/from Longford), and they are quite reliable and inexpensive. What puts me off the car rental option a little is the apparently limited safe overnight parking in the city.
So, I've dome a little research into the walk/bus option, and on the surface it seems quite doable. It's 2.1 km from the airport to the bus stop in Breadalbane, via what appears to be a paved walkway/bike path. That being the case it's less than a 30 minute walk, with a smallish backpack. Once at the bus stop, you have the option of 3 bus lines, namely the 792,794 and 796 to Launceston city. It would really just be a matter of timing your walk according to the bus timetable. I'll let you know what I decide to do in due course.
FWIW, several years ago I walked from HBA to Cambridge to get a public bus to Hobart city, about an hour's walk, past Cambridge aerodrome, which had an interesting and eclectic selection of light aircraft. The things people will do to save a few $$$ (and also keep fit at the same time).