Go into your basement and look up at the floor joists. Wherever the joists span the shortest distance will be the room with the strongest floor framing and wherever the joists span the greatest distance will be the weakest room in the house. (Assuming identical size joists) So the next best location is in the room that has the strongest floor.
Well maybe the strongest room is the kitchen and you don't want to put the aquarium there. So, the best practical position is often as close to a bearing wall or column as possible and oriented perpendicular to the floor joists. That way the aquarium weight is distributed to as many floor joists as possible. And the closer to the wall the aquarium can be positioned the more total weight in pounds the floor joists can support. An aquarium stand with a continuous runner at the bottom will distribute the weight a lot better than a stand with just four legs.
Just keep in mind that if your aquarium is in the living room then the columns and walls supporting your living room floor are below you in the basement. Some of the walls in your living room might be partition walls and not bearing walls at all. It is important to distinguish which is a bearing wall and which is a partition wall.
And that leaves the worst possible position for an aquarium which is parallel to the joists in the mid span of the joists in the room with the longest joist span. There are probably several partition walls that run parallel to the floor joists in the house so don't assume that just because the aquarium is up against the wall that it is necessarily near a bearing wall or column.
Structural framing might be designed for this theoretical uniform 40 psf but it probably doesn't reflect the real world loading conditions in any room of your house. The most likely way for a residential wood floor to fail would be because of excessive shear stresses or excessive bending stresses in the floor joists. So let's say I have a 125 gallon tank and the All-Glass web site says that it weighs 1400 lbs and is 6 ft long. The aquarium is oriented perpendicular to the joists and my floor framing is wood joists spanning 12 ft. So this 6 ft by 12 ft portion of the floor was designed to safely support a total live load of at least 6 ft x 12 ft x 40 psf = 2880 pounds total and may actually be much stronger than that, as discussed above. (And keep in mind that this 2880 pounds includes the weight of any people, furniture, bookshelves etc that are located in that 12 ft x 6 ft area) Does this have much value to you? Yes, but only a little bit. The bending stresses and the shear stresses are distributed much differently due to a large concentrated load like an aquarium than they are when distributed uniformly. Aquariums located close to the wall generate high shear stresses and very low bending stresses. Aquariums located in the middle of the span generate extremely high bending stresses and much lower shear stresses at each supporting wall. But you know that it was easier to break that pencil by bending it, so up against the wall is still the preferred aquarium locatition
Another characteristic of wood is that sustained loads can cause permanent deflections and deflections that increase over time. This "permanent warping" of the wood is called creep. So, if the floor deflects 1/2 inch when you set up your aquarium and you leave the aquarium in the same spot for years that deflection might increase to 3/4". Then when you remove the aquarium you may find that some of that deflection has become permanent. That is why in some older homes the floors are no longer perfectly level.
Article is by Kevin Bauman..do a google search for the rest...I cannnot link to it. THE BEST ARTICLE for understanding tank placement and the engineering.