First, is this a single team or two teams (JV and varsity)?
Without cages, I think that will make it difficult to get in your swings, but I think there are some things you can do. If you have or can find some old netting, you can set up a large net "screen" for lack of a better term. What we have done is just build a frame to support the net, then the net we used was an old cage net that wasn't usable for that purpose any more. This may or may not work in your current situation if you don't have netting. If you can make a screen, you can use this for tee work and soft toss.
Another thing we did was use an old piece of wind screen from the fence to make a solid screen to hit into. We use this for hitting golf balls with a wood bat (note- you have to really keep an eye on the kids for playing home run derby). You could also stock up on regular size wiffle balls, golf ball size wiffle balls, and tennis balls to hit. I've also heard of folks hitting beans, bottle caps, or even a product called hitting disks.
Maybe set up a routine that all the kids go through building up from some of the hitting drills off the field that I've mentioned above, moving on to the on deck circle for on field BP (note here that they should be going through their game on deck preparation mentally) then advancing to on field BP.
Once a guy hits, they are getting live reads on the bases. If you have guys who struggle with baserunning, have them spend more rotations on the bases getting live reads. Also, assuming you have the courtesy runner for catchers, maybe let your catchers run the bases more in practice. Only do this if you haven't really been hard on your catchers during practice because you don't want to destroy their legs. This may or may not really help the catchers, but if they advance to the college level they won't get courtesy runners and maybe it'll help prepare them to run for themselves.
Also, during BP, have your infielders and outfielders in their normal positions getting live reads off the bat. Maybe give them a specific situation they're working on. For example, runner at 1st, less than two outs. Now your infield knows they're rolling two, OF has to read the base hit and decide if they are going to 3rd to keep runners at 1st and 2nd or if the runner at 1st is easy in to 3rd and they have to keep the DP in order by going to 2nd. Have your shaggers deep down the lines and in the gaps so they are out of the way for your live fielders (have the bucket in foul territory down the lines to help your CF get live reads). If balls are clean extra bases to the gap or down the lines or over the outfielders head, let them go and get the next live read. You can have an assistant hitting fungoes to IF when they aren't involved in a live play.
Depending on how much time you have, you could also use this time to get your bullpen work in. Send a pitcher and catcher to the bullpen with whatever their plan for the day is going to be. Obviously when they pitched last and when they are supposed to pitch next will dictate what work they're doing. You can also have a hitter in the bullpen with the pitchers just tracking pitches (also helps give the pitcher a more realistic bullpen with a batter). My personal opinion is during bullpens your catchers are working on everything as if it's live too, so they're blocking and scrambling to recover balls in the dirt. Also, have them work on their footwork for throws to 2B and 3B in the bullpen.
So, now you've got one on deck hitter, one live hitter, seven live fielders, say 3-4 guys in your off field hitting stations, maybe 2-3 guys in the bullpen, and the rest shagging, so I don't think many are standing around doing nothing. Everybody has something to do, and other than shaggers everyone has specific goals they are working on. I'm sure you'll get other better ideas, but this is a start.
Also, one thing to note....if you or someone on your staff can't throw a solid BP, do front toss. Don't waste time throwing one hittable pitch every four throws.