You don't need a special map for the oltrarno. Oltrarno means Beyond the Arno (Florence main river) and encompasses 3 districts: Santo Spirito, San Frediano, San Niccolò. It's just across the Ponte Vecchio.
Main things to see:
Palazzo Pitti
Boboli Garden
Santo Spirito church
Cestello church.
Museo Bardini
Also, up the hill, you can enjoy beautiful views from Forte Belvedere (not sure if open nowadays unless there are special exhibits), Piazzale Michelangelo, Bardini Gardens, and also the upper parts of Boboli gardens. Next to Piazzale Michelangelo is the San Miniato al Monte church, the most beautiful in Florence IMAO.
The locations I just mentioned up the hill are still walking distance from Ponte Vecchio, if you don't mind a bit of exercise walking uphill. If you mind the walk, then a taxi to Piazzale Michelangelo would be best.