Wherever you can get the best price, local coin store, coin show. You could also check some of the online dealers like J M Bullion. J M Bullion posts what they will pay for some coins on their buy back page but you have to insure/mail the coins to them. I would not sell on Facebook or similar and meet someone, just my opinion. Sold coins on
ebay gives a general range of coin values.
There's a big difference between bullion coins and collectable coins with numismatic value. For just bullion coins/bars dealers usually offer to buy at a percentage below daily spot price and sell at a percentage above spot price. Collectible coin values depend on each coin and their condition.
Realize there may be tax consequences when selling. Coins are considered a collectible, the IRS can tax their capital gains. Technically a person is supposed to keep records of what they paid and what a coin sold for. If no records were kept there's a cost basis formula I think. Some people sell coins for cash so no record of transaction but they might get audited and caught. You probably should learn about this before selling.
Also if your aunt is poor and might need to apply for Medicaid in a nursing home the government can go back 5 years checking her finances, if any of her assets were given away, sold. This might change her qualifying for aid.