The second is incorrect.
You may say, "I went shopping for [object] yesterday."
E.g. "I went shopping for apples yesterday."
In a comment I see that someone has indicated that "I went for a shop yesterday" is okay usage. This may be the case colloquially in some places, but I'm not familiar with the usage.
While you will not be misunderstood using either case, and I'm certain you will find plenty of examples of both in current language use. I'd suggest this distinction will always remain clear:
Use in when talking about experience meaning a skill level.
I have 10 years experience in Java, as a software engineer.
This tool should only be used by those with experience in astrozoology.
In these cases you are talking about experience as a quantity, and showing that you want to have a quantity of experience within a certain field/subject. You can also change "in" to "with" for the same meaning.
Use of when talking about an experience as an event.
I was underwater for 10 minutes, I thoroughly do not recommend the experience of drowning.
Skydiving is great - the experience of falling at 100mph is glorious.
In these cases you are describing an experience as an event, where "experience" could be replaced with "phenomenon" or "feeling". As such, you are giving more detail on what the exact feeling was by saying "the experience of falling" etc. Here, experience is not quantifiable, it is referring to the general idea of the event.
Best Answer
The preposition to can work as a shortcut for "which allows access into":
W for X can be used to identify something W that leads to the main purpose or enablement of X. If you buy tickets in order to have access to the concert, saying "these tickets are for the concert" is valid.
W of X means several things, none of which work with ticket and concert.
W of X can mean W belongs to X. Concerts as events can't own things.
W of X can mean W is from X. Concerts as events don't usually generate tickets.
W of X can mean W is part of or made of X. Concerts as events aren't made up of tickets.
W of X can mean action W was caused by X. Concerts don't cause tickets.