I've done a lot of research on this and from what I've found is if you put the length of the tank perpendicular to the joists and against a load bearing wall, you should be ok. Just like previously stated. Perpendicular across the joists and in a corner is even better.
I've searched tons of "180 build" threads and it's pretty much split whether they reinforced the floor or not. I have yet to read a post where someone ended up with their 180 or larger tank in the basement or somehow structurally damaged their floor. I even read a post of a tank build here in Dever where I believe a 300 gal or so tank was placed in the middle of the room with no reinforcement!
Furthermore, I've run into quite a few posts with comments from professional contractors stating a residential floor will handle the weight and more.
This all being said, I just set up a 180 on my first floor and like you, my basement is finished so I don't have access to the joists to reinforce them and didn't feel like putting a steel jack post in the middle of the basement room. I placed the tank perpendicular to the joists against my interior wall which is a load bearing wall. There's a steel W-flange (I-beam) which runs down the center of my house and this is what the tank sits next to.
No problems so far but it's only been 3 months.
HTH