I often paddle the Chicago river. I start off in Ping Tom park in China town. You are allowed to drive your car down the walking path and to the dock where you can drop off your boat. There is a kayak rental service at this location called Urban Kayaks if you're trying to GPS the location. Although they do kayak tours in groups of probably close to 50 boats at a time and in 12ft rec. Boats, I wouldn't recommend going into the river unless you're a little experienced or with someone experienced in the river.
The boat traffic is heavy, and although its a no wake zone and a 5mph speed limit, there's still plenty of drunk boaters flying around creating dangerous wakes and trying to kill you, so always be alert and paddle on the sides of the river and make way for the touring boats. They're moving about 7mph usually. So unless you're really moving they're going to pass you and often. There's other places to drop off into the river. There's Ping Tom Park (by far my favorite); Clark Park off Addison road 7.5miles north of ping tom park, and a public launch off the shipping canal just before the lake under lake shore drive. Parking for this location would cost money and would have a considerable boat carry but then you're in the heart of the city.
Ok, so back to Ping Tom Park in China town... Like I said earlier, you can drive your car through ping tom park to drop off your boat. During times when Urban Kayaks isn't operating, the park district even allows you to park under the bridge in the park. However when urban kayaks is operating, they're going to hassle you, so you'll want to drop off your boat by the river and park in the nearby neighborhood streets or at the park district building. It's at least a quarter mile walk to your car, but parking is free.
From Chinatown, its a 3.8mile paddle to the lock connecting to the lake. The other side of goose island is about 4 miles. On the other side of goose island, there's a couple docks to get out your boat, but neither of the locations are really accessible to anything, just a place to get out and stretch your feet. There's also a bar/restaurant on the north side of goose island. I've checked it out, but not when it was open. You're allowed to use their dock and go in for a bite or a drink, but the place looks pretty classy/hip (like expensive beers and techno music). I'm not sure how catering they'll really be to wet, sweaty paddlers.
About another 3.5 miles north of goose island is clark park. This is where they keep the garage and training facility for Chicago paddling teams, which is definitely cool to see. Another 2 miles north or clark park is where the river forks and there's another park there to get out. It gets pretty naturey beyond clark park, which is pretty especially for people who live downtown and need an escape, but if you're driving downtown to paddle, then you can just as easily drive to somewhere with better nature scenery.
Paddling north from Chinatown, you're paddling right through downtown Chicago. At 2miles from Chinatown, the Chicago river connects to the shipping canal. Heading north is towards goose island and turning east is paddling to the lake. 1.8 miles east and you're at the lake. In the shipping canal, the buildings are tall, the river walk is crowded with runners and tourists and you'll probably get your picture taken by tourists 50times in a day. Just before the lake is another urban kayaks location and a public dock to get out of the water. If you're comfortable with leaving your boat you can walk right onto the river walk and there's places to grab a snack and use the bathroom.
You can get on to the lake from the shipping canal but unfortunately there's no portage that I know of. You have to go through the lock. They'll allow you to use the lock in a kayak, but you're definitely setting yourself up for a sketchy experience. Its a huge lock built for barges. Barges come through, tourism boats go through, and party boaters and yachts go through. On the list of priority, you're in equal terms with other recreational boaters, but most of them don't care if they kill you and many are under the influence and have no idea what they're doing. Be careful when going through the lock. I always go in last as I don't want to get run over. You'll be required to wear a pfd and hold onto the wall via a rope while the water rises to lake level. Make sure you look for a low hanging rope. Most of them are too high to reach in a kayak. Getting onto the lake is pretty sketchy here. You're getting in right by navy pier with heavy fast boat traffic and once you're in the lake, you're committed for a few miles either way and they won't just open the lock for you so you may get stuck on the lake longer than you want to.
My advice is if you're trying to get on the lake from here, know how to rescue yourself if you flip over, don't go out with a recreation kayak, have a bilge pump, also a blow horn wouldn't be a terrible idea. Also be ready for choppy waves over your head. And be prepared in case you get stuck on the lake and have to wait for the lock to let you in. If I go on the lake from Chinatown, I usually just paddle to north ave beach. Its only 2.5miles beyond the lock and there's wave blocks for half of the journey, but again be ready for huge wakes and heavy traffic even with the eave blocks
Overall, the river is awesome to paddle. I probably do it about once a week when the weather is good. I usually paddle on my own. Its nice to go to a place where river current is minimal and there's definitely a lot going on.
I've only been paddling for 3 years and although I tend to paddle about 20miles when I go downtown, I'm no expert. It's probably unsafe to paddle on your own, especially when going through the lock and through the busy parts of the river. Hopefully the information I've given has been helpful.
Be safe, and if you see a kid in a red Epic 18, say "Hi".