As expected, we didn't move up from our lowest lottery pick available. I think there are still a lot of good options for the Jazz. I haven't found all of them, but a few spring to mind.
If Mich PG Burke is still available when New Orleans has their chance to pick, we could trade our two first round picks for that pick. That would be extremely good for NO, and potentially pretty good for the Jazz. Or, we could trade our lottery pick and our 2nd round pick for NO's 1st pick (Burke). That would be a fair trade, but, why would NO want a fair trade when they have a shot at a better trade (with us or others)? One reason for NO taking our 1st and 2nd round picks (instead of both our 1st round picks) to trade Burke would be our projected 1st round pick (Dennis Schroeder, a pg from Germany). Schroeder is much harder for NBA execs (and us) to quantify in terms of future value. IMO, some team is going to get a good PG in Burke, and another team is going to get a good PG in Schroeder.
What I think is more likely is the Jazz keeping their 2 first round picks and going with Schroeder (if available) with our 1st pick and one of a plethora of Centers that should be available in the late 1st round (Cody Zeller, Ales Len, Mason Plumlee, Kelly Olynyck, Rudy Gobert, Dario Saric [technically a SF, but, 6'10'' with talent and a big body] Gorgeiu Dieng, Jeff Whitney, Steven Adams, and Lucus Noguerro).
And, of course, there's the FA Market where we could score a major PG-- leaving us less-reliant on securing a pg in the draft (afterall, Mo Williams would be an incredibly good backup PG). If the Jazz could right the ship regarding a pg in free agency, that would leave a lot of really good options with our draft. We could get 2 or even 3 of the bigs I listed above (getting Saric and 2 others would be a major coup!). This is also a good reason why NO might want to make a trade of their 1st round pick for our 1st and 2nd round picks.
It's very early, but I see a lot of very good possibilities for the Jazz-- more than I see for most other teams.