The local college kids park their $1000 and (way) up Little 500 bicycles in their dorm rooms all the time. Why? Because they don't believe they're safe locked up on the racks outside. That "there wasn't any other place to park the bike" is a problem for OP's case.
Not really. As I said before, the value of the bike is not really relevant to the legal issues. It is conversion if a person steals a $10 bike I left out on the porch, just as it is if I left out a $1,000 bike. While conversion is an intentional tort, negligence is the same way. If there is a duty and that duty is breached, if the breach causes damages we have negligence. Now, we might claim extra steps should be taken with a more expensive item, but it does not really change the underlying issues.
If a new driver is driving along and looks at a pretty girl on the corner (Forgetting we tend to drive towards where we look. Remember your early driving days checking the blind spot?) tapping on the vehicle in the next lane, he is going to be liable for the damages because he's negligent. The issues do not change if the pretty girl is driving the car he taps. The issues do not change if the car she is driving is a Ferrari and the new driver is looking at the car and not the girl. Personally, it scares me a bit that a fender bender that is my fault with an average car might cost me hundreds while a fender bender with a Ferrari could cost me tens of thousands. It doesn't seem fair and there should be some way to minimize the risk of my negligence to reasonably foreseeable damages. But, the forseeability issue gets to duty and not to damages. (aka eggshell plaintiff) There is no shifting of blame for my negligence just because the beauty of the vehicle I hit increased the chance I would hit it.
If there is negligence on the part of the landlord, it is going to be negligence even if a prudent person might have brought up the bike to his room.
Now, an assumption of the risk theory was mentioned earlier if the OP knew the garage was damaged. I think the elements of that would not apply. If I go into a McDonalds in a sketchy area where some hooligans are milling about the front door, that McDonalds will still have the same duty to me if a crime were to happen by a third party as to if I walked into the finest McDonalds in the land. The sketchy McDonalds may have to take more steps to protect from breaching that duty if there have been criminal acts done by the hooligans in the past, but the fact I made the choice to go into the sketchy McD's does not mean I assumed the risk.