You mean you don't have an Aalto vase yet or a Kaj Frank tumbler? What about your mother-in-law?
During the tourist months there is a bus shuttling between downtown and the Arabia factory shop, willing to scoot shoppers back and forth. You may also take the tram number 6. The factory shop stocks first and second grade goods in glass and ceramics. There is also an exhibition upstairs. (currently, July 01, they are having a renovation sale)
Whether you are looking to stock up on your elegant Teema set, or you want just a little something for a friend (I recommend any the glass votive candle holders, very sweet, and not too expensive), or you want to get the biggest Aalto vase ever, you should definately make a visit. Famous Designer Names have created products in all categories, also Iittala glassware and Hackman cutlery and crockery, and young designers have also contributed to products.
If you're looking for something prototypically Finnish to take home as a present: Teema mug with Moomin characters!