Check out encounter tables. They're fun. I know they're in the 2E Monster Compendiums in the back.
Wilderness encounter tables at the back of the 1e MM2.
Treasure tables at the back of the 1e MM1.
Random magic items in the DMG.
Random dungeon map/encounter generator in the back of the DMG.
Monster entries will have a treasure type, percentage chance to be found in a lair (which could be read as the chance to find a lair), and a number appearing for encounters both in and out of a lair. Some entries in the MM - notably for humanoids and giants - will have additional notes about the composition of the group and any pets or allies that they may have. For the most old school feel, abide by the treasure tables, the number appearing and so forth.
It's quite possible to run a decent sandbox campaign with the above tables and a dose of imagination. It will certainly have an old school feel to it as magic items and treasure will be scarce, and discoveries unpredictable.
The random dungeon generator in the DMG is a fun concept, and useful for generating infinitely large mega dungeons with only a small dose of interpretation (knowing when to quit adding doors for example). I used to use it as the basis of 'Open Dungeon Crawl' nights at the local game store. The dungeon it generates is generally far superior to what most newbs will do for their first dungeon and filling a couple of graph sheets and pages with notes from what it generates is an excellent exercise for a young DM.
Second edition is largely a step backwards, but one thing it does have going for it is excellent write ups about the lifestyle and behavior of the monsters. I'd also recommend adopting 2e dragons unless you have a pure nostalga thing going or really know what you are doing.