While not exactly like VLR, both have an overarching mystery to uncover. Corpse Party is like a horror visual novel with some RPG elements (minus actual combat). Ghost Trick is more cartoony and suspenseful, you control a ghost that uses his powers to alter a dead end scenario to continue the plot.
Both are excellent, excellent games. Ghost Trick is one of my favorite DS games while Corpse Party is pretty high up there on the PSP side.
If you have a PC that was made in like the last decade or so there are plenty of fan translated VNs you can get. Console pickings are a bit more limited because very few get official translations. If you liked the puzzles though you might like the professor layton series for DS.