You can rent bikes (per hour/day €3/15) from the TIC. Ask for a free copy of the Cycling Booklet, outlining four themed regional rides.
Central Brežice may not have a huge amount of eating-out choices but a couple of those choices are excellent. Do not leave town without having an ice cream at Gostilna Splavar.
Drinking & Nightlife
The main road through the centre, Cesta Prvih Borcev, has a couple of great cafe-bars with street-side seating that get packed out from early afternoon into the evening.