The winter in La Crosse can be quite severe. People don't like to move during this time of year, which means there aren't a lot of vacant apartments. A better bet is to wait until things start to warm up in April or May before you start looking for an apartment.
La Crosse landlords are happy to work with people to help them find an apartment, but they also have to protect their own interests. You'll need to prove to your landlords that you have the means to pay for your new apartment. Depending on the landlord, this might mean providing a credit report, or a letter of employment that confirms your work situation.
It is easy enough to get around La Crosse using public transportation. The Municipal Transport Utility (MTU) offers bus routes throughout the city. You can also ride the MTU to some of the immediate surrounding communities. The city is large enough that if you prefer to travel independently, having a car is probably a good idea.
Local parks and outdoor recreation areas offer lots of entertainment opportunities near La Crosse. Granddad Bluff is a particularly beautiful spot to visit. The Dahl Auto Museum is a must-see for car enthusiasts of any stripe. There are also local wineries and breweries such as the Pearl Street Brewery or Lost Island Wine