Montjuïc or "Jewish mountain" in Catalan is one of my favourite places in Barcelona. There's a lot you could do here but I like to visit just to take in the views, stroll around the park and have a siesta. Unlike some other parts of the city it's easy to find a quiet corner to enjoy a picnic or switch off here especially if you avoid the times when the Font Magica ("Magic Fountain") shows are on. Not that you should avoid them really, I think it's a great attraction. But seeing that once is probably enough.
Visiting Montjuïc just once however is not really enough in my opinion. Aside from the 1992 Olympic Stadium, you could visit Montjuïc castle, or Palau Nacional the National Art Museum if you wanted to, and that's just three of many things to do. On our last visit, we chose to walk the many stairs (or cheat and take one of the escalators) up the hill from Plaça d'Espanya and simply explored the area for example.
I personally always find myself drawn to the Olympic park. I don't know about you but I always get a sense of excitement when I'm in such an important historic sports site. I do have to admit that I'm a huge fan of the Olympics and the Olympic spirit and love watching the summer and winter games every single time. Standing in one of those environments makes me feel small but also in awe of the physical achievements of the athletes.
When we went here, we went past Palau Nacional and straight to the stadium which was sadly just closing at the time. We strolled past the Torre Calatrava - the big white needle which served as a communications tower during the Olympic games and represents an athlete holding a torch, and stood for a little while by the water fountains where little drops of water felt really refreshing in the summer heat. Then, we returned back towards the area covered by trees to find somewhere to sit down and to fill up our water bottles at one of the many public fountains.
If you are going to Barcelona I highly recommend that you plan a couple of hours or so to come here and take in the atmosphere yourself. Come in the afternoon to hopefully see all the fountains being turned on - that will make for some great pictures. If you do go or if you have been already, don't forget to let me know what your favourite attraction of Montjuïc is.