Many areas of Bali claim to be "the real Bali", but Denpasar, with its crowded alleyways, bustling markets, and growing middle class, probably best represents modern Balinese life. Look past the construction, the traffic and the cellular phones and you will find that the essentials of Bali - the ritual offerings, the smell of incense, and the family temples in each home - have changed little over the centuries.
Denpasar has several good hotels, and a wide assortment of restaurants and shops. Jalan Gajah Mada still has old style Chinese tea shop architecture, reminiscent of colonial Singapore, and a number of fascinating local markets. There are also a number of merchants of Indian ancestry selling textiles. Visit the Bali Museum to develop your appreciation for the Balinese aesthetic, and then visit the shops and put your new knowledge to practical use.
A definite must is the Bali Art Center, which becomes the focus of the island's cultural life every year in July during the Bali Arts Festival.