Lots of USA shows are good for just sorta paying attention to because they are standalone "story of the week" with short arcs to hold things together to add to Monk and Psych there's White Collar, Burn Notice and the most serialized of the group Suits. I'm also fond of parts of Covert Affairs and Graceland. There's also Royal Pains which fits into this same format.
I dropped Covert Affairs when they never answered the "spy in the cold" storyline in like season 2. He comes back, orders Five Guys (

) and then... fucks back off. Never to be explained again.
Burn Notice is fun in a way. But it does spin it's wheels after a while.
White Collar was fun the whole way through, but it's not for everyone. Made me a stan of Matt Bomer before he came out (which was an open secret anyway) due to the shows popularity at the time.
Graceland is from the White Collar creator (Jeff Eastin... same as... Shasta McNasty), but I felt it didn't have the same level of fun as White Collar as it didn't have a "Hook" beyond "FBI agent investigates FBI team that might possibly have a corrupt mole/bad cop in it?"
I watched Suits the whole way through. But really: Stop after Megan Markle and Patrick Adam's characters (Mike and Rachel) get married. The show runs out of gas and doesn't know what to do with itself at that point to where Gina Torres got a spin-off (which got cancelled last year due to low ratings and... not being a lawyer show.

) in one of the seasons as a back-pilot, and then the creator finally gave a (really rushed, IMO) "will they or won't they" romance to Donna and Harvey, and the lawyer that got shat on for a bunch of seasons finally gets a true-love and a baby on the way. If you MUST watch after that Mike/Rachel episode, watch the season finale only, because the rest is "whatever" but the finale (while rushed) gives a conclusion to most of the series regulars (though Markle is only mentioned in passing, and Patrick J. Adam's shows up for a little bit, thankfully).
Monk and Psych were a little before these other shows, so they don't have the same USA-isms in them.
(I watched a lot of USA in high-school until late 10's/ until Mr. Robot finished on the network. Now I don't.)