This is probably a dumb question, but what are the rules regarding commas after which or where?

I am under the impression that a comma is needed when we're referring to a specific place. For example:

1. "I went to my friend Paul's house, where we played a lot of video games." (comma used)

2. "I went to a park where people could feed the duck." (comma not used)

I believe a similar rule is used for which: the comma is not needed when it is used in the context of "that."

1. "We stayed in the Ritz-Carlton, which is a really nice hotel." (comma used)

2. "We stayed in a hotel which had a low rate." (comma not used)

However, I've seen many people omit the comma for the first case. Can anyone confirm if my examples are correct?

Your examples are correct. You can study the use of the comma in relative clauses in any good grammar book, and you'll probably fine examples and rules online if you google for "types of relative clauses". You'll learn about restrictive or defining clauses and non-defining clauses and the use of commas in them.

thank you
this is very helpfull