Thailand is pretty much the last place to go for cakes and pastry of any kind. If you ever joined a Thai birthday party you will likely remember the margarine-like paste that passes for whipped cream more than anything else. At the more fun & rowdy birthday parties this paste is then used to smear on other peoples faces, indeed a better use for it.
Fortunately, all this is changing. Little cake & coffee shops are mushrooming all over the place, and are becoming very popular among the young and middle class, as well as foreign visitors of course. One of the nicer of these places is Love at First Bite. Their motto is: "To be happy for an evening, get drunk. To be happy for a week, get married. To be happy for life, visit Love at First Bite." 8-)
They do a good variety of cakes and pies. You can get takeaway, or eat in the very clean and bright airconditioned garden house or in the garden itself. This nice setting for an afternoon tea makes it one of the better places in my opinion. The cakes at the Sheraton Hotel bakery probably have the edge, but this place wins hands down on atmosphere and cheerful service.
If you're ordering for a birthday party then you probably want to order a whole cake in advance. Or you can get it by the slice, most cakes go for 50-60 baht. The place is on the Old Chiang Mai - Lamphun road soi 1. When crossing the Nawarat bridge coming from Thapae Road, turn right onto the Chiang Mai - Lamphun road, then it's the first soi on the left, before you get to the Chiang Mai TAT office.