You can paint in any area where you have the space- kitchen, office, dining room, outside. The key is to create a way that things can be set up easily, so that it doesn’t take all the fun out of it for you. And, to create a space that lets the toddler have freedom to make a mess so that you can relax and enjoy watching them play or even work on something else of your own (collocated of course).
I use two old sheets as drop cloths, one for the floor and one for the work space. The drop cloth on the floor I have completely under the table, which does involve moving the table but is worth it when I can relax while she’s painting instead of watching like a hawk. If it’s a multi-day project I just roll it up and leave it under the table. The second sheet goes over the work surface and down on all sides. Because I’m using sheets I make sure they are doubled, a single layer would not provide enough protection. If the area was too big to do that I would use real canvas drop cloths, which are not too expensive and worth buying if you plan on doing lots of projects. I have two; one for messier things, and one for cleaner things. They are well worth the money. I keep my two craft/toddler drop cloths in a crate with all our painting supplies. It’s all very easy to pull out, set up, and start making a mess.
Tip – If your little artist suddenly decides they are done painting and has paint out that cannot be covered and saved for another day just pop it in the freezer. It can be removed from the freezer, left out to warm briefly and used again.