Sapporo is small. You can practically walk everywhere, and walking is actually part of the fun particularly if you are not used to snow. But still, you have to go places and based on my research, here are the options one has:
Subway Pass. Unlimited for JPY830 a day (less for weekends and holidays)
It only applies to the non-JR subway trains. Each ride is around JPY200, so you need to ride it at least three times to break even. Is it worth it? Not so much. Unless you wanna go all over the city, I don’t think you’ll ride more than thrice. For example, I went to Sapporo Dome (first ride), went to Susukino Street (second ride), then went to Sapporo station (third ride) to go to Otaru.
JR Welcome pass. Unlimited for JPY1,700ish a day.
If you are coming from the airport in the morning and exploring, or going for a day trip to Otaru, this is the way to go.
The catch? Your visa should be temporary visitor.
Chitose Airport to Sapporo.
You can take the train (JPY1,500ish) or the limousine (JPY1,030). If you are qualified for the JR Welcome pass, take the train. Otherwise, take the limousine (which is really a bus).