Jhansi is a compact city; the main sights cluster around the fort hill and are walkable from each other if you don't mind unshaded streets and occasional traffic. In practice, most visitors use auto-rickshaws for the fort-to-museum-to-Phool Bagh circuit. Rates are negotiable; agree a price before you get in. The fort, Rani Mahal, and Phool Bagh can be covered in a half-day by auto if you keep moving.
Cycle-rickshaws work fine in the old bazaar areas — the lanes around Sipri Bazaar and below the fort are too narrow for autos in parts. For the cantonment cemetery and outlying sights, an auto or taxi is more practical.
App-based cabs (Ola, Uber) have a presence in Jhansi but coverage is patchy. Your hotel can arrange local drivers for a fixed daily rate — useful if you plan the Orchha day trip, as public buses to Orchha run infrequently and a private vehicle gives you flexibility over timing. The Jhansi-Orchha road (about 17 km) takes 30–40 minutes.
There is no city bus network worth using for tourists. The railway station is the logical hub; hotels in the station area make it easy to combine early-morning departures with an evening return from Orchha.