Your hotel is at the corner of State and Ohio, it is north of the River in the River North area. It is NOT in the Loop or very near Millenium Park/Grant Park.
Cabbing to MOSI from the Mag Mile area would cost you a fortune; don't do it. As the PP noted, take the #10 CTA bus. You will have to either go east to Michigan Ave or South down State Street to the Loop to catch it. The route with the least walking is probably to get on the Red Line subway at State & Grand, ride down two stops to Monroe and cross the street to the bus stop. (You could also leave the subway at State/Lake, but that's a large transfer station, so you would still be walking a lot, just underground.) Getting to the Field (and Shedd) is just as easy, take the #146 Museum Campus bus from Michigan at Ohio. Both of these special bus routes will deposit you right across the street from the museums you want to go to.
If you haven't ordered your CTA visitor passes yet, do so right now. It's much more difficult to get them after you arrive, as the machines at Union Station (and MDW) often run out during summer tourist season, and when that happens you need to visit a CVS store to buy them.) When they mail the tickets they will also send you a nice central city transit map you can study, or you can download it at:
http://www.transitchicago.com/assets/1/brochures/13JN_017-DTSSG.pdf
One special note: if you are planning to visit the major museums on a summer weekend day, be prepared for the possibility of having to stand in line to buy tickets. Shedd, especially, can have a wait of up to three hours in the ticket line. This is where the CityPasses or membership passes prove their worth, because you can skip that line.
One little fun thing I recommend: splurge a bit to take the water taxi from the Museum Campus to Navy Pier (the Chicago Children's Museum is excellent). It's a short boat ride that the kids will love, and is faster than any transit on land -- it also gives you a lovely view of the downtown skyline.
If you are not used to subways, here is a little tip: carry a pocket compass. (A real one, not the compass app on a cell phone). It will help you determine which exit to take to leave the station to point yourself in the correct direction that you want to go once you are above ground. This is because the station exits are labeled with which street you will emerge on, but if you don't know the streets well, you won't know if that street will put you N, S, E, or W of the station.
Also, if one of you will be carrying a smartphone, there are several apps that help with CTA and cabs in Chicago, see this article for reviews:
http://www.chicagobusiness.com/article/20121012/NEWS07/121019931/navigating-the-navigation-apps (There is also a cab app that lets you specify number of passengers:
https://hailocab.com/chicago)
