With the army of umbrellas out there these days, make sure you know the rules.
Those umbrella stands that are outside every store or resto are no guarantee that you'll see your prized umbrella ever again. Taiwanese have a nasty habit of swiping others umbrellas.
A lot of long time foreigners here have just given up. In fact, I suggest using and re-using one of the plastic bags people put over umbrellas that you can find at the door of more reputable establishments.
Umbrellas are on sale everywhere but generally you can buy one for less than NT$100. Fancy ones are more but don't let them out of your sight! If you do you'll be doing more bargaining with these ladies!!!