Let me know if you need any assistance in Andover.
First let me say that I have family in Andover, and I think Winchester and Andover are both lovely towns. However, a quick google maps research will show you that you commute will be over 1 hour from Andover, and worse from Winchester. As noted on these posts, 495 to 290 will work from Andover, but there's no real good way to get from Winchester to Worcester. Traffic is not your problem, but distance is. My office has a saying that towns in Mass are like flavors of ice cream, they are all different, and not everyone likes the same flavor. If you let the group know what type of town you are looking for, they can help you best, and I would also recommend mentioning how much time you want to spend in the car. I agree with Wendy that Natick has a very straightforward commute to Worcester, but I think Dover would add a lot of unnecessary minutes. Natick and Andover are similar in size, schools, and feel. (Similar is not same). I think that even Natick would be too long for me (about 40 minutes) , but I am not you! I suspect that you have family or friends in these towns, hence the favoritism, but I think even they would admit that the commute will be difficult. There aren't too many communities that have the same "feel" as Andover along 495 en route to Worcester (most communities are much more rural, with smaller populations), but you might find some that are close enough to your liking. Shrewsbury has good size (35,000 people), excellent MCAS scores, and reduces your commute to 10 minutes, but it will, of course, increase your commute to Andover and Winchester. But with all the time you save, you'll have extra time on the weekends to go see friends and family in those areas!
It's your choice - make the best one for you and your family.
It sounds like you have some idea of the area. If you want to plan your trip out you may find this link helpful http://www.mapathon.com/ma.shtml. I'm with Irena, unless there is a need to be in Andover or Winchester you could find something closer. I have a system that can create a community report on any city/town. If you want to research some other places e-mail them to me and I can send you back the reports in a PDF format. You can also request one on my website linked below. Good Luck!
If you do persist than Andover is your better bet in terms of commute, since 495 is right there. If you go with Winchester than you will have a longer commute.
I actually commuted from Andover to Worcester myself, but that was over 10 years ago, and during typical am/pm commute times. Rt.495 (then Rt.290) is really your best bet from Andover. It was long, and often busy on some stretches, but certainly not nearly as bad as Rt.93 or Rt.95/128 can be (the Turnpike is further south, so you wouldn't do that from Andover anyway).
I also used to take a little known-detour for the latter part of the trip, taking Rt.2W from 495 to Rt.190S, right into Worcester ... this stretch was much easier and quieter - and more scenic - than Rt.495/290. If you're going to Worc. mid-pm though, I don't expect you'll have typical rush-hour traffic issues.
Hope that helps. By the way, I'm a REALTOR in Andover ... feel free to contact me if I can ever be of assistance, email@example.com. Good luck!