The best Tennis Shoes for Arch Support are Asics Women's Gel-Kayano 26 Running Shoes and also New Balance 680v6 Running Shoes.
These running shoes are also Tennis Shoes and are very comfortable shoes and are good for walking, jogging, running and even playing sports such as Tennis.
I have the New Balance 680v6 Running Shoes and they are very comfortable and I can wear them all day without my feet hurting.
Also if your feet do hurt some you can use some gel inserts for your shoes to help with sore feet.
If you're on your feet a lot then using the gel insoles will make even the worst shoe feel great.
Buying a more expensive shoe can help your feet be more comfortable and help with playing Tennis as well.
Nike Also makes a good line of Tennis Shoes, Running Shoes, Jogging Shoes etc.
They are more expensive but they are well worth the price and will last longer than cheaper shoes as well.