My youngest child's favorite activity is painting. I remember back when my first child was 3. I was very nervous around painting projects, but now that my third child is 3, I have become much more relaxed and have found that there's nothing a little soap and water (and occasionally a whole bath) will get off. I have also found that an old adult-sized T-shirt makes a great cover-up to protect clothes. Painting outside in the lovely fall weather can be relaxing and fun.
Try making apple prints with apples cut in half. If you cut the apple along the equator you can make a print of the star! You can tape leaves to a piece of paper, paint over them, and then remove the leaves to reveal their outline. For some sensory as well as visual projects, squirt some washable tempora paint on a clean Styrofoam meat tray, and have your child squish her feet in the paint and then step on a big piece of paper, walk in a circle, or print some dance moves. Develop vocabulary and imagination by talking about how the paint feels and what the prints look like. Or, with a shiny paper plate resembling an artist's palette and a squirt of each primary color, your child can use his fingers to discover what happens when you blend colors. (Have a bucket of soapy water ready outside to wash up.)
No matter how many great projects I come up with at home, sometimes my youngest insists, "But mom, I just want to play with other kids." On one of those days I often check out what my local MOMS (Moms Offering Moms Support) Club is doing. Almost every town has one that you can join. They offer playgroups, outings/trips for the kids, and special interest groups for moms as well. It is an excellent resource for meeting new friends and finding inexpensive activities you and your child can enjoy.
Your local library has a lot quality free programs to offer as well. In addition to library sponsored story times and crafts, many libraries host outreach programs for babies through preschoolers such as playgroups and "Play N Learns" by Community Partnerships for Children, and Music and Movement classes through the NRC Family Network, both funded by the MA Dept. of Early Education and Care. Both are fun, valuable experiences for children and their caregivers. Each program encourages caregiver-child interaction and gives you ideas to continue at home. Check the library's bulletin board for dates and times. Remember, you are not limited to your own local library. Check out libraries in surrounding towns for a wider variety of opportunities to meet your child's and your schedule's needs.
My youngest especially loves to visit the Children's Museum in Easton. In addition to the fun, developmentally appropriate exhibits, the Museum also offers a wide variety of classes. Pee Wee Singers and Music Makers, Pre-Ballet, and Friday Frolics are perfect for toddlers and preschoolers. Click here for a complete fall schedule. The Museum is also a great place to meet other kids and their caregivers...while big sister or big brother is off meeting new friends at school.