I have baseboard heaters in my main living space. I can't see for sure without taking the covers off (which I haven't done yet) but it appears 2 copper pips come up from the basement (through the hard wood floor) to power them and the holes cut seem to be WAY too big around the pipes (fingers could absolutely fit in the spaces). To prevent rodents from coming up from the basement and to just have a tighter living area altogether, I'd like to close these gaps safely. I know there is foam out there and steel wool is also an option, but are those really safe for use around what I assume would be hot pipes? I also read about something called an escutcheon ring but for some reason, I'm seeing those as being $10+ piece and I'd likely have to 10-15 of them (maybe I was looking at the wrong thing). Any suggestions would be great! Thanks.
A metal escutcheon ring might be sufficient for your purpose. I would fill the hole with steel wool to stop the mice, then cover with silicone to prevent a draft. The steel wool might be unnecessary, as I don't think mice will gnaw though silicone. However, if the hole is large, the steel wool would make it easier to fill it with silicone without having it fall into the basement.
Don't use spray foam such as Great Stuff around heat sources: it will melt and produce toxic fumes.
BTW, the reason the holes are so big is probably because there used to be three-inch pipes there. Such pipes were used for steam systems and for pump-less hot-water systems where the water was circulated by gravity (convection).
I would use a plastic or metal escutcheon as suggested by others, however I would make sure that the escutcheon did not fit up tightly to the sides of the pipe. That is to say, leave a small gap of about 1/8 of an inch between the inside of the escutcheon and the outside of the pipe. You can use silicon to secure the escutcheon to the floor.
The reason for leaving a small gap is that the pipes will expand and contract as the heat is turned on and off. The gap will prevent any friction between the two items. If they do rub, you will hear the rubbing every time the pipe changes temperature.
Do you have space to install a floor flange trim plate? These should be available in a variety of sizes, so you should be able to find one designed to fit around your pipe's OD. They are made from different materials and different shapes (plastic versions should be way cheaper than $10). It should look something like this: