Park Street & Queens Road and Gloucester Road & Stokes Croft are both areas in Bristol that are safe and tourist friendly. Both areas are filled with shops, cafes, bars, restaurants and other attractions to fill your day with. If you fancy some classic retail therapy with known brands, Park Street & Queens Road is your destination. Gloucester Road & Stokes Croft is recognised as the more indy sector of Bristol, with many independently owned, vintage or charity shops residing there.
By all means, explore other parts of Bristol but these densely populated areas should see you almost certainly safe (Keep an eye out for pickpockets though!).