Hi folks! General hardware question, and I may be in over my head.

One of the prime camping locations at a nearby park is unfortunately
in a valley. This has the effect of radically limiting our GMRS
radios.

Would it be at all useful to run a mobile or base antenna about
50 feet up a tree and leave an antenna line so that we can just
plug in when we're at camp to get in contact with folks out
in the bush?

Quite possibly so, if your feedline has low-enough loss.

GMRS is a UHF frequency, which propagates mostly by line-of-sight.
There's some diffraction around edges, and some amount of reflection,
but as a general rule you can expect a better signal (somewhat-better
to lots-and-lots-better) if at least one antenna is up out of the
"ground clutter".

Feedline loss, on the other hand, will work against you. Thin
feedline will eat up a lot of your transmit power and your received
signal... e.g. ordinary RG-58 will lose about 6 dB (that's 75%) of the
power in a 50-foot run. That might, or might not, overwhelm the
advantage of having the antenna up at some height.

You can get the loss down to 4 dB by using RG-8X "mini" coax.
Standard RG-8 cable will lose 2 dB, which ought not to be a problem.

A decent combination might be to use a GMRS base antenna which has a
few dB of gain, and a run of RG-8X (which is fairly light and
unobtrusive). The antenna gain and the feedline loss might just about
cancel out, giving you something roughly equivalent to what you'd get
if you were standing up in the tree with the radio :-)

Can anyone make a suggestion as to the right hardware for the job?
Is this a scenario where I'm going to need to "tune" an antenna?

If you buy a pre-tuned commercial GMRS antenna and its usual
installation kit (which may include pre-tuned radials), it'll probably
be a "wire it up and go" job, with no antenna tuning required.

Be careful to take all of the appropriate precautions - e.g. a
climbing belt/harness, safety rope, and so forth. A distressingly
large number of amateurs are killed due to failure to take proper
safety precautions when climbing towers, buildings, and so forth.

Also - for legal reasons, this sort of antenna mod can only be done to
a real GMRS radio, for which a GMRS license is required. It's not
legal to modify the antenna setup on an FRS radio.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
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