It always crashes in buy mode, and always when I try to put down a table or a chair. It crashes even when I put down something that's Maxis-made. I don't think I can do the "empty downloads folder" method because I have mods with custom NPCs and memories. My game was working fine until this week. Will I have to reinstall?

It honestly sounds like a mod issue. I'm not sure how custom NPCs would work in this case, but I would do the 50-50 method anyway by making a backup and not saving when testing.

Do a backup of your game (in case you get any problems). Take out everything except NPC mods and memories (these are not too likely to be causing problems, and shouldn't be removed once you've put them in) and other essential mods that's best to keep in. It's a good idea to have a folder for mods you know you should not remove from your game even when testing CC (name it "EssentialMods" or some such).

Run the game with just these mods, check if the problems are still there. Game running fine without crashing? Then you move on to 50/50 testing, but keep those particular mods in. As long as those aren't the ones causing problems, you should be good to go.

If you added any CC the last week or so, try to move out these files and see if this helps. It's always a good idea to have a "quarantine" kind of folder, where you put new files to see if they work alongside the rest of your downloads, and if they do you can put them wherever they fit. Especially if you go on large downloading sprees.

Reinstalling is not necessary if it's a CC issue. It's rarely if ever neeeded (actual reinstall is rarely needed for other things than if you're installing on a new computer or after a full OS reinstall, if game files have become corrupted somehow - which is actually not very common, or if you've installed lighting mods and similar in the install location but didn't backup the files and want to reset to "factory settings"). Most of the time it's your saved game that gets corrupted, which you can do a "soft reset" or by renaming the TS2 folder in Documents (for backup purposes) or moving/deleting it. The folder will regenerate with a brand new untouched game.

However - in your case, it's most likely a CC issue, so I don't think you have to worry about a full or "soft" reinstall. Could be an idea to test in a "throwaway" neighborhood, though, one you can delete when you're done testing, or use for testing purposes later.

I just did that and nothing is crashing. Now to find out exactly which file is the culprit.

I think I found the dastardly piece of CC that was causing problems.