The RS London guidebook advice to see the Crown Jewels first was absolutely correct on my visit. Unlike the poster who said:
And, though I'm sure I'll be flamed for this, the crown jewels were just okay. Lots of glitter and quite beautiful, obviously. I didn't care for the presentation, too fast and crowded, as well.
I found seeing them absolutely worthwhile and one of the best things about the visit to the Tower. But that might be due to the fact that I showed up early in the morning to the Tower just before it opened and while everyone else immediately went and started jockeying to get on the first Yeoman Warder tours, I skipped right past that and went straight to the Jewels and, aside from the one guard stationed in the room where the jewels were kept, I was the only person there for a good 15 minutes so got to look at them for as long as I wanted. When I left there, I went to get on one of the next Yeoman Warder tours and was able to get hooked up with a tour group fairly quickly. Shortly after that, the place was packed - but after my tour was over, it didn't much matter. I spent a few more hours just checking out some of the other buildings on the grounds.
The next time I plan a trip to London, I would most definitely try to get tickets for the Ceremony of the Keys. With your trip scheduled for just a few weeks away, it won't be possible as they are already booked months in advance, but it's something to note for a future visit.