Herculaneum is unjustly less famous than its bigger brother -- though considerably smaller, its buildings are better preserved and mosaics/frescoes remain in situ. Herculaneum didn't suffer such bad structural damage, but it lay in the path of a pyroclastic flow -- mud and lava devastated the area, pushing the nearby shoreline back by 500m. Rediscovered in the early 18th century when a well was dug (the town had been buried over 20m deep; hence the excavation lies in a bowl, surrounded by the rebuilt town), word spread and most valuables disappeared; proper archaeological excavations began in the early 20th century.
Take the Circumvesuviana railway to Ercolano Scavi station, tben walk 1km down the hill. Herculaneum's main area comprises two broadly parallel streets (Decumanus Maximus and Inferior), bisected by three narrower streets (Cardo III to V). It's compact -- a walk will take 1-2 hours; the buildings are well-preserved, so assume everything is worth a look.
Decumanus Maximus was the gracious main street, partly closed from traffic as a Forum. The teatro was partially excavated in the 18th century; lying slightly north of the Decumanus Maximus, it held 2,500 and was fairly unusual in not being built into a hillside, but free-standing (like Rome's Colosseum).
Along Cardo IV, the House of the Mosaic Atrium has a tablino (living room), garden, terraces, and halls with rich paintings. The nearby Casa del Tramezzo di Legno (House of the Wooden Partition) and Casa Sannitica have wonderful atriums and fine frescoes; the Casa della Gemma (Jewelled House) is distinctively painted in red and black -- the kitchen hearth holds crockery remains.
From the House of the Stags (Casa dei Cervi), containing some remnants of statuary and marble furniture and an impressive atrium with frescoes of deer being chased by dogs and a Stairo con otre (satyr with wineskin) statue, there's a ramp to the so-called Sacred Area (which itself has steps down to the old harbour and the arched storerooms) where about 300 victims of the lava flow were found during excavations (closed to the public). Next door, the House of Neptune and Amphitrite contains beautiful wall mosaics -- this quality is what makes Herculaneum stand out from Pompeii. Look also for the fresco of Hercules (after whom the town is thought to have been named).
The Suburban Baths (sometimes closed but very well worth seeking out) are well preserved, particularly the floor mosaics -- look at the floors: the weight of the flow caused the tesserae to crack and the floor level to subside. Three distinct rooms can be seen -- tepidarium (warm room for acclimatising), caldarium (steam-filled room), and frigidarium (cold room for a quick plunge in the pool); it still feels like a place to socialise in grandeur.
The vast Palaestra (gymnasium) saw exercising and athletic competitions; surrounded by three columned walkways with portico and loggia for spectators, you can also see the remains of a meeting hall, supposedly where athletes received their traditional olive-wreath crown (cut from the wild olive tree from which Hercules' clubs were made).