Cetinje  is the historic capital of Montenegro. The city is of enormous historical and spiritual value to Montenegro. During the siege of the Ottoman empire, Montenegro itself had, at numerous times, been reduced to just Cetinje and its surroundings.
Cetinje is a town of 19,000 located in the small valley under the Lovćen mountain. It was founded 15th century by Ivan Crnojevic. His son founded the first printing house in the South Slavs. Due to the strategic nature of Montenegro, it being an independent state on the border of the Ottoman Empire, all of the major European powers had an embassy in Cetinje. For this reason the town has a continental style old town located a thousand miles away from any of the continental cities that the architecture is representative of. It is very much the spiritual heart of Montenegro.
Maybe the best way to get to Cetinje. It is less than hour drive from both Podgorica and Budva. Buses to domestic destinations are very frequent despite the fact that the bus station does not have a ticket counter (you can always buy your ticket on the bus though!).
All roads in Montenegro are two-laned only, and mostly curvy mountainous roads, so speeds over 70 km/h (43 mph) are rarely legal, and rarely safe.
The road from Kotor to Cetinje is a curvy, mountainous road, and mist or ice are not uncommon. The road from Budva to Cetinje is in relatively good condition with 3 lanes in some parts. The road from Podgorica to Cetinje is in fairly good condition.
Cetinje, especially the historical center of the city, is small enough, and everything is within walking distance.
There is a cummulative €10 ticket that allows you to visit all the museums in Cetinje. You can buy the ticket at each of the museums.
Visiting Cetinje is really about understanding Montenegro and it's history.
If you are looking for a genuine Montenegrin souvenir - Cetinje is the town! Other than that, Cetinje is not really a shopping resort, leave that for coastal towns or Podgorica.
Cetinje is the right town to try out traditional Montenegrin cuisine, e.g. veal filled with chese and ham. Despite the name of the country, make sure you try the excellent Adriatic fish and seafood.
Montenegrin quality wine is a must-try. The best known Montenegrin wines are the premium "Vranac", "Pro Corde", "Krstač", "Cabernet", "Chardonnay" and the famous home made Crmničko red wine.
Grape brandy (rakija) "Montenegrin loza", "Prvijenac", "Kruna" or home made grape brandy (lozova rakija, lozovaca) is also great.
You cannot find private rooms in Cetinje as easily as in other, more touristic, Montenegrin towns. There are two places that offer rooms for rent next to the bus station (you need to go left from the bus station and then take the first right). Once you get there you will need to call the owners the phone, because they're usually not there. The rooms are really nice and cost €12-15 per person.