Neve Tzedek located in South Tel Aviv is filled with small shops and cafes (another nice area to just wander). Shimon Rokach was the first head of Neve Tzedek and he built a house in the area in 1887. His granddaughter restored the house and it now serves as a museum open to visitors by advanced arrangement. However, I recommend buying tickets for the evening show. Actors dress up in character and circulate throughout the house followed by a performance in Hebrew that depicts life during that time period. A very enjoyable night.
Rokach House - 36 Rokach House - 03-516-8042