The Moder Tales of Faerie series by Holly Black (Tithe, Valiant, and Ironside): Very similar to Mortal Instruments in style.
Speaking of Mortal Instruments, have you read Cassandra Clares new book Clockwork Angel yet? If not, you should! I personally think it's even better then the first.
You could try The Meggie Quinn: Girl Vs. Evil series by Rosemary Clement Moore. It's about a girl with mild psychic powers who fights demons.
Maybe try Scott Westerfeld? He's not *as* romantic as, say, Hunger Games, but there is a little and his books have a lot of adventure... a lot of people suggest the Uglies series (which is sci fi, like Hunger Games, though NOT a similar plot or anything), but I prefer either Midnighters or Peeps. Midnighters is about a group of kids who can access the "secret hour" because they were born exactly at midnight... and they fight evil stuff and try to figure out more about why the exist and what they can do and so forth. Peeps is a vampire story that goes off of the idea that "vampirism" is actually an STD type of virus that's affects are similar to rabies. The hero, Cal, is infected with the disease but is only a carrier. He works to capture others who are infected.
Somebody else already mentioned Percy Jackson, which I will go ahead and second. It's pretty good.
Devilish by Maureen Johnson
The Wicked Lovely series by Melissa Marr
The Need Series by Carrie Jones (*slightly* Twilight-esque, but not as bad as some other paranormal romances and has a bit more action. Also, it's not vampires.)
If you think you could stomach some stuff set in a past time period/ alternate universe you could check out:
Libba Bray's Gemma Doyle Trilogy
Tamora Pierce (author, lots and lots of books)
Diana Wynne Jones (try Howl's Moving Castle of Darklord of Derkholm)