If I can pull it off, I'd like to do something that actually may have an impact, namely leaving a legacy for our race for others to find.
Before everything shuts down, gather data on our species and the state of the Earth, along with whatever information I have on our downfall, heavy on the history and culture, but also plenty of technical and scientific data useful for an industrial age civilization. Most of it gets recorded on storage drives sealed into vaccum sleeves. The most critical items also get recorded on nonreactive metal tablets, including technical data on how to read the drives (in case the included equipment fails in spite of precautions), and a crash course on the English language (baseline words are given using math concepts and images to give the potential reader a place to start). The whole cache gets buried in an environmentally sealed room built under a geologicaly and meteorologicaly stable region. If feasible, I would also remove the oxygen from said room. I'd probably leave at least three such caches to be relatively sure
Given all too much time and quite literally all the resources in the world, I shouldn't have a huge problem getting that much done, assuming I'm lucky enough to keep my health up for a decade or two. Making sure the time capsule gets found is the tricky issue. A physical marker on the surface is pretty much guaranteed to be completely useless after only a few thousand years, much less 100 million, the minimum time I'd be shooting for. It should be possible to leave a multiple frequency beacon that only activates when it detects non random transmissions. But while we have some equipment that comes close to the right level of durability if well protected, powering it, even passively, is a huge problem. I'd be doing my homework in any event, perhaps a solution would pop up from out of our long list of green projects that aren't feasible for high energy use.
I'm well aware that the odds of any such effort paying off are extremely low, either in terms of a new civilization arising on Earth or the planet being scouted by outsiders, but I'm not the type to just give up and die, and there certainly wouldn't be much else to live for in such a scenario.