Thanjavur's reason to exist as a travel destination is the Brihadisvara Temple — the Great Chola monument that has dominated the city for over a thousand years. But the Royal Palace complex, the Saraswathi Mahal Library, the Art Gallery, and a scattering of smaller temples give you at least two full days of material.
The city is compact and walkable in the historic core, though auto-rickshaws are faster in the heat. The main temple and palace complex are within a kilometre of each other, making it easy to cover both in a day.