Near Needham there are several nice places to dance; I recommend the following:
In Dedham, Moseley's on the Charles is a large, elegant ballroom which has live bands every Wednesday evening at 8 p.m. and a lesson at 7 p.m. For further info: www.moseleysonthecharles.com or 781-326-3075.
In Newton, Balera dance studio on Rumford Avenue holds public dances every Friday evening from 9-11:30, with a lesson at 8:30 For further info: www.baleraballroom.com or 617-969-2280.
In Norwood, there's a dance every Sunday evening (with some exceptions) at the Knights of Columbus Hall on Nichols Street with a lesson at 5:30 and dancing 6:00 to 9:30. Please check the website at www.norwoodsundaydance.com.
For info on other places to dance (e.g. there are special dances held weekly for Swing and West Coast Swing), go to www.havetodance.com.
The website of the greater-Boston chapter of USA Dance is www.Massabda.org. Click on Events on the left side of the main page; then go to Dances and Parties; then click on Donna's List - a very detailed list of dance venues by date.
If you have any questions about the above, I would be happy to answer them if I can!!