OK so your interested... sold on the idea that reupholstering an vintage chair is a better option that buying something mass produced from the high-street... but no you don't have a beautiful victorian chair just sat their begging for a new look. Hears my top 3 places I would advise you to start your search.
Remember to look past the horrible fabric and look at the shape of the piece, check it is the right size for you (older furniture can be on the small side!) And check the frame is sturdy, a little wobble can usually be fixed but if joints are split or broken it may be beyond me to fix it!
ANTIQUES MARKETS
Going to big markets can be overwhelming but a great place to start even if your not quite sure what your looking for, theres always a wide array of stuff ranging from every period so it can be a great place to start to under stand what your drawn to and like the most.
Atlas Antiques website does a great job of listing most of the markets going on around the country and is worth a look hear ...
As I am London based Sunbury is one of my faves which is held at Kempton race course on the second and last Tuesday of the month, top tips is to get there early and take cash!!!
Specialist charity shops
If your not so bothered about an actual antique and more interested in getting an old frame to give some love why not check out your local charity shops, there are often ones that specialise in furniture often British Heart foundation have shops that are specialised in furniture, you can check where your nearest one is.
Again all the same rules apply and the main thing to look for is a sturdy frame. Who knows you might pick up a designer piece at a bargain price :)
Ebay
So every one has some sort of relationship with e-bay, tbh its not my favourite place to spend my time, and I really prefer to feel the frame and chair in person, but it can be great if you have a specific thing your looking for an you can set up an alert. Remember to check the pice for wobbles before paying and be wary if something seems too good to be true, Ercol's and branded things that are super check may not be what they appear. As well as Ebay Facebook market place can be a great place to pick up cheap or even free pieces that are local to you.
If you want to discuss something before buying, take a few pics, including the bottom and send threw to me for an idea of how much the upholstery would be.