There are a bunch of things it could  be, but let's start with the cheap. If
you've recently changed transmission oil to a product like Redline, that
could do it. In some cases, Redline makes the synchro rings too "slippery"
to restrain the gears, which then don't mesh right especially under
acceleration. Other than that, it sounds like the synchro rings themselves
are bad, but it could also be a number of other things in the tranny. Really
doesn't matter at that point what it is, because you have to pull the
tranny, take it apart, replace what's bad, and by then you're into it well
over $1,000 no matter what's wrong with it. Given this, it might just be
better to learn to live with the grinding. Especially if you're just driving
it around town.

I'm not an expert,though, and I'm sure others will have more to say than I.

Good luck with it.