The first date is the 27th of this month, ie Wednesday next week, when we will have the Queen's Speech. Government departments are beavering away, each writing their contribution to the Speech. The Speech will translate election promises into Acts of Parliament. This is when we see what our new Tory government actually plans to do.
The second date is the 8th of July. This is when George Osborne will present yet another Budget to parliament. Given the two month delay it looks this is more of a challenge than the Queen's Speech. Of course GO has already had one bite out of this cherry because he presented a budget back in March. But it seems that wasn't a "for real" budget, just a showpiece to get some votes in. Back in March this blog noted we are now doomed to have one of these faux budgets every five years. Any new government would certainly want a new budget, and it seems the loss of the Lib Dems is enough to invalidate previous plans.
That said, the most significant date on the horizon is Autumn 2017, precise date not yet decided, when we will vote on whether to remain in the EU. We can expect major drama in the run up to that date.