We've had good experiences with Family Healthcare Associates ###-###-####, they have two offices: 302 King Farm Blvd, Suite 130, Rockville, MD and 20528 Boland Farm Rd, Suite 104, Germantown, MD). As far as a hospital is concerned, we haven't had to use them, but we've heard Suburban is good. For after-hour care, we had good experiences with Secure Medical Care, ###-###-####, 803 Russell Ave # 1, Gaithersburg, MD 20879. This might be far for you, but our son liked Rockville Nursery School & Kindergarten, 301 Adclare Rd, Rockville, MD 20850 ###-###-####. If you just want your kids to have a little structured playtime, you might want to look into the City of Gaithersburg's Casey Community Center preschool. My youngest liked having preschool "at the barn." http://www.gaithersburgmd.gov/
Hope your move goes well!