Ok, so the first thing to remember is that this is temporary. If you want to work towards earning money to get a house or flat, you can do it. That should in fact be your primary goal.
At 3, your child won't really understand the situation so as long as you stay cheerful and happy when you have your time with them, then the child will also be happy and enjoy their time with you.
Some ideas are going to the library....most librarys have a good children's corner with nice seating and books to look at together. Many also run pre-school singing and storytime sessions which are free. You can ask at the counter about this.
You could spend an hour in a library quite easily, it's warm, safe and there's stuff to do...and free!
Other ideas are going on nature walks in your park or local woods or other natural beauty spots, show your child all the flowers, leaves, plants and things that grow. If there's water, throwing in stones and sticks amuses toddlers for ages.
going to a cafe for a drink if funds allow...same with swimming, look to your local leisure centre for lower prices. Some have a cheap membership deal so you can get a pass.
Do you work at the moment?