Wyndham is probably the best bet for location if you need a kitchen. We live in the suburbs and go to the city overnight pretty frequently. I normally just use Starwood points or Hotwire/Priceline and stay in a regular hotel, so we don't end up with kitchen access. The Hotel Blake does come up in RCI from time to time, so that would be another option. No kitchen, but it's a nice hotel in a decent location. I've stayed there in the past and enjoyed it.
In terms of activities, I completely agree about Museum of Science and Industry. It's a great place for kids or teens. I'd also recommend at least one day at the museum campus (Field Museum, Shedd Aquarium, Adler Planetarium). You can get one of those City Pass-type deals and do all three. They are all great. I'd also suggest one of our zoos. You can take the Metra (suburban rail) to Brookfield Zoo, which is a truly excellent zoo, but it is pricier. You could also take the Red Line (CTA) to Lincoln Park Zoo. It's much smaller, but it's still a nice zoo, and it's free. I'd also do a stroll through Millennium Park, which is another free activity. You could do one of the observatories at Willis Tower or John Hancock. I normally prefer the Hancock building, just because the lines are generally shorter. If you do that, you can also do some shopping (or window shopping) on the Magnificent Mile. Very touristy, but still fun. I'd also consider trying to get same-day discounted theater tickets. By April, Lake Michigan and Chicago River cruises should be up and running again, so that is an option. The architecture tour might be a good choice for teens, but they are all fun.
My only caution is that our April weather can be very questionable. It could be 70 and gorgeous, or it could snow. If you have any outdoor activities picked, I'd definitely have an indoor plan as a backup. Brookfield Zoo would be an exception, as there are many indoor exhibits, so you can be comfortable even if it's chilly. We even go in December and January when it's freezing.
I don't know of any particular gluten free restaurants, but I think most are pretty accommodating, so it shouldn't be hard to find workable food options.
