昨日(の?)走っていたのは難しかったです。
The running we did yesterday was difficult
I'm unsure about the の after 昨日 here because I've always been taught to just leave it dangling without a particle. I'm pretty sure you can throw a で on there if you please, but in this case I felt like a の would work because I'm specifically talking about the running that happened yesterday. Ergh. So many things to be cleared up.
I don't think の would go after 昨日; as you said, there is no reason to put anything after it. Perhaps what you are confused about is the way that の can replace が in a relative clause (a clause that decribes a noun and acts like one long adjective). For example:
経験がある。 I have experience.
経験がある人。 A person with experience.
経験のある人。 A person with experience.
経験のある人を求めています。 We are looking for a person with experience (an employer's position, perhaps).
At the end of a sentence, you would use が here. But, if the same phrase becomes a relative clause, you can use either が or の。 In the same way that の can be used to have one noun describe another, it also can replace が in adjectival phrases like the one above.
Aside from the problem with の, this sentence seems very wrong. 昨日(の?)走っていたのは難しかったです。
For one thing, running is rarely, if ever 難しい--perhaps if there are a variety of moving hurdles, it might qualify. You probably mean 大変。 Also, the 走っていたのは is ponderous.
I imagine something like 「昨日は大変でしたね」 would be more than sufficient.