There's a huge transit center parking lot a block away from the Atwood Building, as well as lots of parking across the street at City Hall.  I'm sure something can be worked out for parking.  

But the real question is why they need a large building in the first place?  Legislative session is held in Juneau where there's already a perfectly suitable (and newly upgraded) capitol building.  Each legislator should rent a modest office, or occupy an office in an existing public building (state, city, Tribal, school...) in their own districts where their constituents can actually meet with them face-to-face.  

When they want to meet with each other, use teleconferencing equipment like the rest of the corporate world is going to.  If they're going to hold occasional public meetings, hold them in a school auditorium or public library.

Granted, this will make it harder for the lobbyists to do 'bulk purchases' in one convenient location.