I don't think there are any bard instrument quests at that low level,
except for the Vah Shir ones.

As for dropped instruments:

Drums: Mistmoore Battle Drums, or Stretched Skin Drum should be
possible for a group of mid-to-high-30s, but it's probably easier to
just get 100pp to buy them in the bazaar.

Strings: Combine Lute or Combine Mandolin, vendor bought in Katta
Castellum, there is nothing dropped that you can do that's as good.
If you really don't want to pay money (50ish pp), you can get one in
Mistmoore.

Brass: Torin's Horn from Torin in Echo Caverns, or a Combine Horn from
Katta Castellum.

Wind: modifier doesn't matter, just get a wooden flute.

You can also start saving up for LDoN instruments, and while you do
that you might get lucky and have an instrument from a named.

The only quest for an instrument I'm aware of is the Nostrolo Tambourine.
http://everquest.allakhazam.com/db/quest.html?quest=427
I'm not sure whether you can do that at lvl30something. And it definitly
is easier to camp the money needed for a trueborn drum of the dark rites!
But if you want to do the quest just to do quest stuff then go on and
have fun. :)
Btw, for other instruments I have some recommendations though none is
for a quest. For wind I'd try to get the bloodied flute. It costs mere
10 points in MM LDoN and is primary slot only.
For brass I would go for a troubadours mace. Unless you want to AE kite.
Then you should look for a high brass mod.
For stringed instruments I have no real outstanding recommendation. ;)
The combined instruments from Katta Kastellum are quite nice though.

Hagen