The organizations renting your facilities should also be customers.  But the customer center really isn't meant to be used the way you're using it.  Customer should be the name of the donor or organization, use the customer type field or create a custom field to categorize them into donors, private parties, etc.  Both are located on the Additional Info tab in the customer records.  I recommend using the type field for donors and facilities and create a custom field to categorize the type of facilities (private party, etc.)

You're using classes appropriately, except I recommend making a specific fundraising event a sub-class under Fundraising rather than a Job.  You should use Jobs for grants though.  Establish the granting agency as a customer and list each individual grant from them as a Job.  If they are multi-year, you should also set them as a sub-class under Temporarily Restricted funds, which is where you book the revenue.  As you spend down the grant, you transfer the funds to your operating fund.

Are you using Premier Nonprofit or Pro?  The online version is similar to Pro, but I usually recommend Premier Nonprofit for nonprofits because it's got some really useful reports and Word templates not found in the other versions.  If Pro works fine for you, than Online will as well.  But there's a monthly subscription fee, so you may find that it's more expensive in the long run.

Let me know if there's anything else we can help you with!