Hmm, there have been some pretty fantastic films that were Oscar nominated, across a pretty wide range of genres too. I know based on your posting the type of movies you tend to like, but I wouldn't avoid a film just because it's "critically popular" otherwise if you're really into film, you're missing out. I was curious, so I looked at the 2010s Oscar noms list on Wikipedia, and just pulling out a few examples:
Inception
Toy Story 3
The Social Network
Django Unchained
American Hustle
Dallas Buyers Club
Her
Nebraska
The Grand Budapest Hotel
The Imitation Game
Whiplash
Mad Max: Fury Road
The Martian
Arrival
Hell or High Water
Get Out
Lady Bird
Keep in mind, I'm also a big fan of foreign films, indie and subversive anti-industry material, love me some Shaw Bros too
These are movies that I've seen at least once, would highly recommend, and
in bold are ones that we [usually own and] have watched at least 5+ times. We've got action/sci-fi, animated/kids, horror, black comedy, drama, lots of overlap, all ranges of budget, etc.