The 2015 MLB Draft order has been determined. Once you get beyond the 1st round, things get a little messy for a while, between compensation picks and competitive balance picks, but here's how the draft will begin:
2. Astros (for not signing 2014 #1 pick Brady Aiken)
7. Red Sox
8. White Sox
18. Blue Jays
While I'd rather have seen the Indians go 85-77 than 73-89, those couple extra wins a month weren't quite enough to get them into the playoffs (a major disappointment), but they were also enough to move them from the top ten of the draft down to #20 (a minor disappointment).
The Indians have only had the 20th pick once before, but it worked out well. The year was 1998, and the Tribe selected a high school pitcher by the name of Carsten Charles Sabathia.
The Indians will also have the sixth (and final pick) of Round A of the competitive balance selections. That's currently slotted as the #37 pick, but will almost certainly move down a bit, due to some teams gaining a compensation pick for losing a free agent who was made a qualifying offer. Last year the sixth competitive balance pick ended up being #40 overall. Those competitive balance picks are the only type MLB teams are allowed to trade, so it's possible the Tribe will move theirs, but I wouldn't bet on it.
Most likely they will have a pair of picks in the top 40 or so, with their next pick (in the 2nd round) coming in around #60, followed by a 3rd round pick somewhere between #95-100, with remaining selections to come every 30th pick.
If you don't feel it's too early to start thinking about potential targets, you should check out Kiley McDaniel's top 51 prospects list at FanGraphs, which includes brief scouting reports. At the top of his list is Brendan Rodgers, a high school shortstop from Florida. At #20 on the list is Kyle Cody, a 6'7" RHP from the University of Kentucky.
The 2015 MLB Draft will begin on Monday, June 8.