Lease up for renewal – advice for negotiating?

So, my apartment lease will be expiring in a few months. I got a renewal offer today. My rent won't be increasing but it's not going down either.

I'm not totally surprised by this, but I was hoping they would at least knock off $100/month. I currently pay around $1050/month. It's a "luxury" apartment (aren't they all "luxury" these days?) but doesn't have any special amenities.

I've been searching around this past week and it seems like most places are dropping their rates. In fact, my complex is advertising units that are the same floor plan as mine for $800-900/month on their website. Of course, a rate on a website doesn't mean much. It can always change. Also, I realize they want to offer lower rates to new tenants, but they probably want to milk me for more money since they know moving is a hassle.

I want to try to negotiate with them. My complex is owned by a big corporate company, so I expect they are unlikely to waver. Here's what I have on my side:

1) One of my neighbors is being evicted. They haven't paid the last two months of rent, and didn't get assistance. I imagine other tenants are in a similar position, but I only know about my neighbor. This might mean they're desperate to hold on to good tenants.

2) I have always paid my rent early. I have been a good tenant – not hassling them for anything and not causing any problems.

3) I am actually willing to move if they won't budge. I think they are counting on me not doing my research or being complacent, but I'm not going to pay $1050 if I can move a block away and pay $700-800.

I'm not certain of the best way to approach this and would appreciate any advice you can give.