The easiest place to take a dip from Tinos town is at Kionia, across from the site of the Temple of Poseidon, 3km/2 miles west of Tinos town. Another beach close to town lies 2km (1 1/4 miles) east of town, at busy Ayios Fokas. West of Tinos town, a series of hairpin-turn paved and unpaved roads lead down -- and when we say "down," we mean "way down" -- to beaches at Ayiou Petrou, Kalivia, and Giannaki. From Tinos, there's bus service on the south beach road (usually eight times a day) to the resort of Porto, 8km (5 miles) to the east. Porto offers several long stretches of uncrowded sand, a few hotel complexes, and numerous tavernas, several at or near the beach. The beach at Ayios Ioannis, facing the town of Porto, is okay, but you'd be better off walking west across the small headland to a longer, less popular beach, extending from this headland to the church or Ayios Sostis at its western extremity; you can also get here by driving or taking the bus to Ayios Sostis.
There are two beaches at Kolimbithres, on the north side of the island, which are easily accessed by car, although protection from the meltemi winds can be a problem. The smaller has more wind protection, beach umbrellas, a changing hut, and two tavernas. Just beyond Pirgos, the beach at Panormos is on the verge of turning into a holiday resort, but has a decent (usually windy) beach and several good fish tavernas, notably Agoni Grammi (tel. 22830/31-689). If you eat here, be prepared for cars and buses to come very close to your seaside table.
Tinos is a walker's paradise, with a good network of paths and remote interior regions waiting to be explored. Some of the best walks are in the vicinity of Exobourgo -- paths connect the cluster of villages circling this craggy fortress, offering great views and many places to stop for refreshment along the way. There isn't a current English-language guide to walks in Tinos, but most decent maps of the islands indicate the paths, many of which are the former donkey and footpaths that connected villages.