During weekends and free days you can do some exploring and check out the surroundings. Here is two possible options.
The first option is Mbudya Island. First you have to get to the White Sand hotel and from there you can get a boat. Return ticket costs Tsh 10000 and Island fee is Tsh 20000.
The Island itself is nearly a paradise. White sand and warm turquoise water. You can pay for the sundeck, but I did not even consider this, because for me the whole point going to the beach is to get your tan on the sandy surface. You can also do some nice snorkeling in the clear waters.
Food on the Island is great. You can get a good size plate of fish or calamari and chips for Tsh 15000. Soda will cost Tsh 2000 and beer Tsh 4000. If you leave after the tide has started to go out, prepare to walk in water and mud as the boat is not able to come to the shore.
The other option is to go to Bagamoyo. To get there from Madale, you have to go to Tegeta first and take a local bus. This daladala will cost Tsh 2000. Drive takes usually about 45 minutes, but can last hour and half if the traffic is bad.
Bagamoyo is an old town, where slave trade was taking place. In the 18th century and 19th century Arab slave traders took huge numbers of slaves from Tanzania to European colonies in the Indian Ocean. Mainland Tanzania was under German rule from 1890 till the First World War. Then Tanzania was handed over to British rule. You can still see old ruins from German and British colonial periods.
In national holidays it will be packed with local people. Food wise there is lot of fish food available.
If you are planning to go to Bagamoyo you should reserve the whole day just in case. Visiting museums and ruins in Bagamoyo will require you to pay entrance fees and hire a tourist guide. You can make these trips independently, but Art in Tanzania can also arrange hassle-free trips for you with a car and a driver.