Remove it for another variety. I always think local nurseries know best. Keweah is supposed to be a great flavored yellow peach. If you are set on white fleshed try the Babcock.

http://www.berkeleyhort.com/edibles_fruit_tree_list.html

Here is a link that might be useful: East Bay Nursery

Or graft a different peach onto it.

Unripe peaches I would think would taste sour, even whites, it's ripe, it's just not that good. Go for one with a better acid-sugar balance. Yellow fleshed types usually are. White are usually low acid, and to me i relate that to no taste. others love it, but you know what whites taste like now. Some exceptions, Indian Free, Indian Cling, and Artic Jay are whites with a kick. Facist Nation gave good advice.
You know the grafting is a great idea, you could actually graft a number of cultivars unto the tree to check them out.

the grafting suggestions are the best option. I don't have time to find the video right now maybe someone has it bookmarked. It is a dude from a professional orchard grafting over a not-so-good peach into some other things. It is severely cut back to short stub scaffolds leaving a small original branch, called a nurse branch. Once the new varieties have some volume the nurse branch is removed.

Your tree has a great root system that will grow the new varieties much faster then if it has to establish roots

Dave Wilson has such a video on their site.

Local nurseries only know best if they are passionate about fruit trees. Maybe that's a common occurance in CA but as rare as unicorns in NY. Here, if a local nursery has any peach trees it will probably be Reliance.

A beginner might as well buy a new tree- at least if they possess the average wealth of citizens of the bay area. I bet there is a nursery that specializes in larger, ready to bear trees from Dave Wilson's collection somewhere not to far. I'd choose one of the highly rated white nectarines if I wanted white flesh.

Great feedback, thanks. If i were to try my hand at grafting, where would I find the scions to use?
Strangely, the local Costco seems to have a great assortment of mature peach trees in stock right now, about 10 different varieties which is more than my local nursery.

I agree with Harvestman.
We have three local places that sell fruit trees.
Two know nothing and one tries but you will get better advise from the many experienced fruit growers on this forum.
If it doesn't taste good or produce, etc, etc. then re-graft if the rootstock is favorable.

I'll have to agree with the others who have suggested grafting. Not only will it be your cheapest solution, but it will likely involve the least amount of work (compared to growing an entirely new peach tree).
As for where to find Scions to use, do you happen to know anyone that owns a peach tree? If not, you could ask the local Costco you mentioned if they would allow you use their mature peach trees. It wouldn't be the first time I've heard them allowing this.

Here is a link that might be useful: The Peach Tree

With peach trees an established tree doesn't save you much time over a new one. With any other species of common fruit I'd consider an established tree more of an asset. Whether you graft has more to do with whether the experience holds interest for you than anything else, in my opinion. Most people would cut down the tree and plant anew, from my experience.

Those Cosco peach trees could probably deliver good crops by the second season- possibly more quickly than grafts. For pears or Euro plums a new tree might take 7 years to crop well so grafting could save significant time.

However, if you graft, you have the opportunity to put 3 or 4 varieties of your own choice on a single tree. That would allow you to spread the harvest and probably make better use of the fruit as well an taste different types.

Thanks again. I'll read up on grafting as it's always something I wanted to try, but as the days fly by and I never get around to it, I'll probably end up just planting a new one.

It sounds like your tree was a failed graft at the nursery that they did not catch -- your tree is the rootstock. I had a few of those myself and they were all super fuzzy, tasteless, and small.

Scott

Great catch Scott. You know Lovell is supposed to be a cling peach. Wonder if that is the rootstock?

Lovell is a yellow cling peach. I wonder if the OP's peach is just some random seedling rootstock.