This is speculation, but there are a few reasons why she might have given him the diary. Feel free to pick your own winner, or perhaps it could be a combination of them all.
Personally, I think the most probable reason that Emily gave Will the diary to give to Summer was safety. With it being so irreplaceable, it is very likely that Emily (or even Summer) didn't want it being sent by post, where it might be lost or damaged. I don't think there was any urgency for Summer to get the diary back, so it is likely Emily was holding onto it until she next saw her, but when Will is traveling to the same city as where Summer lives, it makes sense for him to take it back to her instead.
Another possible motive could be so that Will could meet someone, anyone, whilst in New York. He was traveling to a new city, where he wouldn't know anyone, so having a pretense for visiting someone and possibly gaining a friendship whilst living there would be a good motivation.
Alternatively, for Will's line of work it would be very beneficial for him to get contacts that he could trust. A journalist would be a very good contact to have, so it is possible Emily wanted him to meet her in order to help him with his career.
Considering that Will was planning on marrying Emily, it is not entirely unreasonable that Emily was having the same thoughts. As Summer is clearly a very good friend of Emily (she had trusted her with her diary, and they had kept in touch despite living in different cities), it is possible that Emily wanted Will to meet her simply to get to know her, as she was an important part of her life.
I was under the impression that Emily slept with Will's roommate whilst they were living in different cities. Even if she was planning on sleeping with him and wanted to ease her guilt about doing so, manipulating both her boyfriend and (best?) friend into sleeping with each other seems entirely underhanded and out of character for her. Whilst it isn't entirely out of the realms of possibility, I'm going to go with Occam's razor and say it isn't the reason.