Many shops would install a cassette bought from them for free or maybe something like $5.00. The chain install wouldn't be a freebie, but again fairly nominal if bought from them.
As for the actual parts themselves they vary significantly depending on the model. If you have a bike co-op in town that would be your best bet. If not look for what I call a "blue collar shop". By this I mean a smaller shop, with maybe not as nice a location, which sells more intro and mid level bikes vs. high end, and where repair and service are a bigger part of the business.
The actual price of the same parts may not vary tremendously, but the labor charge will.
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