I'm doing a complete rewrite of this post as I found a better (cleaner) way to do this via an app. My initial post was using an app called Tweetcaster. It worked well enough and offered a free version, but there were some quirks with the filtering that made it a bit cumbersome. This way is MUCH easier.
- Click Menu in the upper left.
- Then Account Options at the bottom.
- Select Mute in the middle.
- Under the Client section, click New Item.
- Enter "foursquare" as the new item (no quotes).
- Follow the upper left breadcrumbs back to your timeline.
That's all there is to it. Now you can enjoy a check-in free timeline! You can also filter out anything else you want based on it's application. For example, to filter Gowalla checkins, just enter "gowalla" as the Client - since it is the Gowalla app that sends those tweets.
By the way... if you find yourself swamped with checkins from your friends and do not want to have to filter them all out - you may also consider suggesting to them to not share every checkin to Twitter in the first place.