I am traveling to Basel (Switzerland) this summer and wish to take a day-trip to the Niesen Mountain. Can I go there by public transport, how much would it cost?
There is a cable-car going up to Niesen Mountain. As the Wikipedia article says, it is one of the longest cable-cars in Europe.
An overview about the prices is available on the official homepage. You should look for the station at the top of the mountain which is called Nielsen Kulm. The price is around 53 CHF for a return ticket if you don't have any reduction price plans.
The funiculair starts at Mülenen which is rechable by public transport from Basel. Checkout the official SBB homepage, and you will see that you can get there in 1h46, changing the train once in Berne, for a total of 112 CHF (retour ticket).
So in total you will have to pay around 165 CHF for the whole trip. Keep in mind that there is the so called Halbtax Abo in Switzerland that costs 150 CHF and allows you to use all the trains and a lot of cable-cars for half of the price for a whole year. So if you plan to do more such trips, it can be worth to invest in such an card.
In this particular case you would already save 82.50 CHF. So if you think you're going to spend another 135 CHF for train tickets in the next 365 days, I would recommend to buy a Halbtax Abo.