How common is it to be able to find good cappuccino in coffee shops in Thailand? Are coffee shops common in Thai cities at all?
Although nowhere near as ubiquitous as in the US, coffee shops are relatively common in major Thai cities, especially those with high tourist numbers (eg, Bangkok, Chang Mai). In addition to over 100 Starbucks stores around the country you'll also find countless McDonalds, many of which have "McCafe" and - depending on the area - many western style coffee shops serving your choice of various forms of espresso and drip coffees.
When ordering it's worth making sure that you're getting what you think you are. "Cappuccino" doesn't vary around the world as much as some other drinks, but there are slight variations between countries (and often between shops in the same counties!). Starbucks has the edge here in that they will almost always make the US version of a drink regardless of what country you're in.
Expect to pay about the same as what you would in the US, which means that your morning coffee could well be the most expensive thing you buy all day!
For a start, Starbucks Thailand exists. So if you're desperate, at least you know you can get a recognisable drink and service at that. It's like McDonald's, as a tourist you don't usually want to have it, but at least you know what you're getting. And they do have cappuccinos ;)
There are many, many coffee places here at the moment. Thailand goes through full-on phases - last year there was the fish massage parlours (i.e. you put your feet in a tank full of fish that eat the dead skin) - it was such a good business for 5 minutes that every other shop became one (they were even in Tescos!) - now they are all but gone. Right now there are wall to wall coffee places, many are already falling away (expensive equipment and lush set-up can not hope to be covered in 40baht coffees from passing Thais and tourists - and too many places to charge more!) All the usual coffee types are available - although I find mostly the coffee used for espresso is a bit on the weak side compared to say France or Spain (where the best coffee is served IMHO).