There are a bunch of ways to learn Go. If you are interested in getting together with individuals for live play and instruction, there is a Go club in the Cleveland area that was being led by Eric Lee (etxlee@gmail.com) out of Case Western as recent as last April. The American Go Association Club Database has more details. If you are willing to travel, my club in Columbus would be happy to spend some time with you and your kids teaching the game. Details on our club are also available online.
There are a lot of resources available online. Consider starting at this interactive tutorial. Then move on to the AGA website for a bunch more links and information. Other places online I like to go include GoDiscussions.com and Sensei's Library. Sensei's library can be difficult to follow at times, but has a nice section that is organized for beginners.
Once you have a handle on the rules, you might try a few 9x9 games with a computer opponent. Actual games are played on a 19x19 grid, but the best way to learn is to start on a smaller board. IGoWin, a free version of the ManyFacesOfGo program, is available as a small download and can be a good, free opponent for your first 50 games. There is a Japanese Go proverb that says to lose your first 50 games as fast as possible, so don't be discouraged if you don't win at first. It just takes some getting used to. Note that IGoWin also has a decent online tutorial.
After you are comfortable, you can take your play online. There are two primary ways to play online - turn-based and live. The most popular live play system is the Kiseido Go Server (KGS). There are players of all strengths on KGS, including many younger players. You should have no problem getting a game. However, if you are like me and don't always have time for live games, you can also use OGS or Dragon Go Server. Both let you start games and play single moves at a time. The system emails each player as their turn becomes available. Since you are only playing one move at a time, you can get a bunch of different games going simultaneously.
If you and the kids are enjoying Go, you should probably get yourself a board and stones. There are many low-cost boards on the market, including some at specialty toy stores. I found my first board at Larson's Toy Store here in Columbus. However, I would not recommend these options. The board you get isn't worth the money. For a small amount more, you can get much better equipment online. I would recommend Yellow Mountain Imports for good selection and prices. Something like this set is a decent price and value. They also have a nice beginner set that is printed with 9x9 and 13x13 grids.
The only other resource I haven't really talked about is print materials. Not too long ago, you couldn't find anything about Go written in the English language. That has been changing and now there are a bunch of books available. Many beginner's find Janice Kim's Teach Yourself to Play Go series very helpful and you can easily find it online or at some brick and mortar stores like Barnes and Noble. I particularly like Charles Matthews' book Teach Yourself Go.