I cycled through Montenegro as part of a touring trip about 5 years ago. Travelled from Pogdorice up the Moraca Gorge and Tara Canyon (scenic routes) to Durmitor national park and camped at Zabljak. This looked like a ski resort, so it was pretty quiet in summer, but did some nice walking on waymarked trails in the mountains.
Travelled south from here to the coast. Lots of lovely quiet back roads and wild maquis countryside if you get off the main routes. I visited Ostrog monastery, which is built into a high cliff, and stayed in their dormitory for a few Euros. Lovcen, the Black Mountain, is worth a visit for the summit viewpoint, which gives fantastic panorama views of the surrounding area and the Adriatic coast. There's a nice hairpinned descent to Kotor Fjord (largest fjord in southern Europe), and it is not too far over the Croatian border to Dubrovnik if you have time for a visit.
I thought it was a lovely country, and would certainly visit again if I had the opportunity. It's also worth reading up on your Balkan history to get the most out of your visit.