The Castle (Ljubljanski grad) is visible from almost everywhere within the town which bodes well for the view from the top and means it's a must-visit. It was apparently built on a prehistoric site on top of the hill in the Middle Ages; the info within the virtual reality museum in the tower (included in the price for climbing the tower itself) will tell you that the earliest reference to it dates from 1144 -- the Odalreich of Ljubljana -- and that records show that it was first used as a fortress, later as barracks and that the present, quintagonal, irregular layout is of later origin. In the 13th century, the castle was the defence core of the town and protected the local peasants until 1797, the year when the French, under Napoleon, first captured Ljubljana (look out for Napoleon's golden face on the Illyrian monument in the university/parliament area).
In the 1500s, the castle underwent some reconstruction works by Italian architects, Spati and Decius -- in 1544, the provincial governor took up residence and had the defences fortified. In 1686, the gunpowder tower exploded and, in 1782, the castle building ceased to be functional until transformed into a prison house which it remained until 1849. In 1905, the local government decided to use it instead as a cultural centre and accommodation, which is why the (continuing) works began (and it's not apparent when they will end). These days though, it's also used quite heavily as a civil wedding venue and a procession of different brides wandered past while I was there on a Saturday afternoon.
And, sure enough, the view does live up to expectation -- a fantastic panorama across the city. It's even worth climbing up the hill rather than taking the tourist "train", to see the vista open up as you gain height. The path up is signposted from the town-centre, and diverges about half-way into either a slow-but-steady or steep-but-quick route, so can you take your pick. Either way, there are some obvious stopping points and benches to have a breather on the 15-20 minute walk/climb. When you reach the castle, you'll see for yourself that the renovations are ongoing still, and that the only accessible parts are the tower and courtyard that you cross to access the tower. (Note: the courtyard has a fairly good lunch restaurant/coffee bar -- I'd particularly recommend the delicious iced coffee on a hot day to regain your strength before tackling the tower's spiral staircase.)
In the basement of the tower is the Chapel of St. George, apparently first mentioned in 1489 and re-done later in Baroque style. The impressive coats-of-arms of Carniolian provincial governors, on the walls and ceiling, date from 1747 (though they appear to have been touched up much more recently than that). It's pretty bare apart from the shields and escutcheons, but there are pews to sit on while you crick your neck at the ceiling.
Then it's time to climb the pentagonal tower for the view -- eagle-eyed visitors will already have noticed the marvellous dragon brazier at the entrance where the (long-gone) drawbridge and portcullis should be. A second dragon is sighted on the Ljubljana flag, flying from the tower, and the third is beneath your feet as you climb . . . take a closer look at the iron stairs and you'll see him again, aloft a crenellated turret.
The castle is open 10am until dusk and the cost for entry to the tower (including the virtual museum -- the chapel seemed to be free anyway) is about £2.50/$3.50 for adults and about £1.60/$2 for concessions.
(Note: the other great city-viewpoint in the rather ugly black Neboticnik highrise which dates from 1933 -- at the bottom, there's a sign "Kaverna" and a lift to the top-floor terrace where you can eat or drink coffee. It's not too expensive and the view is free.)