For "Me pasé el resto del día en un sobremesa con mis amigos.", how about:

"I spent the rest of the afternoon/day just shooting the breeze* with my friends around the dinner table".

*"shooting the breeze" is an idiomatic expression for a relaxed conversation.

It appears that there's no exact translation.

I found this though that talks about "hacer la sobremesa"
http://forum.wordreference.com/showthread.php?t=5256

What are some other example sentences in spanish of how you would use sobremesa?

There's not really an equivalent in English for "sobremesa". "Lounging" or "to lounge" is a similar idea, but it doesn't specifically convey something that you do after a meal.

Thanks a lot Mike and torusan.

Thanks a lot torusan, but I have a question: how can I translate the word in the sentece that I used.