Offhand, can't think of much that 350 will get that you'll get a lot out of. Maybe Burnt Chest Wraps (stam clicky) or Mummy Wrappings. You might get extraordinarily lucky and find someone unloading a Damask Leather piece (not the tunic), but 350 might be a stretch. Dragonsteel Bracers is another option. If it's really just burning a hole in your pocket, then maybe pick up some low-mid tailored/tradeskilled pieces.
My 2 cents, hang on to the plat - maybe save up for a nicer piece later. In the meantime, you can complete your starfall, do newport ring up to III, and maybe even some lower level quests (Erudin Symbol of Honor) or lower named (Vulfwere Fur Sleeves) -- stuff that is soloable at your level. In a few levels (maybe towards low 40s) you can start the Monk Wyvernfang Sash Quests.
Edit: Sharkskin Shoulderpads is an easy rec since it's generally pretty cheap (15-20pp way back when - not sure of current market). If you can't find one on listsold, you can prob hunt the skins (starfall) and ask/pay for the assistance of a tailor.