Sorry, not sure but is very close to town centre

Battery point itself is a nice neighborhood so you could walk around and enjoy the buildings, the water fronts, and also on clear-days the view to Mt. Wellington. Salamanca market (only on Saturdays) and Salamanca place area is nice with plenty of diners and cafes. From Salamanca place you could easily walk to Brooke St Jetty areas. There is dedicated shuttle to go to Mt. Wellington which could be booked at the tourist information centre. If you go to information centre there is 'Tours Tasmania' company which provides many day tours option (start as early as 7-am pick up and return to Hobart in the evening round 6-7 pm, check out the brochure which is available there). Tasmanian Museum and Art Gallery is just very close to the information centre and it's free entry. If you would like to do some 'museum marathon', the Maritime museum (with entry fee) is also nearby and the Mawson's Hut (with entry fee) is right at the corner. Another option is the art museum MONA (also with entry fee for tickets and trip there could be via a dedicated ferry or shuttle, tickets could be purchased at their counter inside the Brooke St Jetty). Port Arthur is another good historical site but you might need to book a tour there combined with other destinations to seize the day (I tried the 'Port Arthur & Tassie Devils' day tour and quite like it). If you are into some walk-amongst-nature, visit the Royal Botanical gardens (1-2 hours inside is sufficient). My faves are the Japanese garden and the sub-arctic house. From inside the garden there is great view to the Tasman Bridge as well. Regarding the day-tour, I also like the 'Mt Field, Mt Wellington & Bonorong' day-tour, with some light range of walking inside the trails and a visit to Bonorong wildlife sanctuary. I hope you could use some ideas now to explore and enjoy Hobart.

There is a lift at St Ives Apartments in Battery Point