Presuming that you don't want the coat to reflect 'honorable scars from fair wear and tear', I see no reason why it couldn't be done almost invisibly.

 

Do you think that this would be an inexpensive repair (<$30-40)?

 

If you’re going to have it repaired, you should use a professional re-weaver.

As to cost, you’ll have to get an estimate.

 

Just as a matter of interest, do you know how the damage occurred? Here's hoping you don't have a moth issue!

 

My experience is there are two ways to go. A reasonably competent tailor can sew it to minimize its obviousness (since tweeds hide imperfections well) and to prevent any further damage and that, in NYC, can be done for around $20-$30. And it will be fine as long as you don't want perfect and it isn't in the most obvious place on the jacket.

The other way to go, as suggested above by SG_67, is "invisible" weaving which, my experience has been, will make it all but perfect (no one will ever notice it again), but in NYC, that would cost closer to $100 (and that's just a guess as you need to get an estimate and sometimes my guess for invisible weaving is far off).

Good luck in whatever direction you choose to go.

 

I reweaved a small rip on my wool pants and it cost me $60.

 

Two three threads from the hem and reweaving is easy.