A good rule of thumb is to provide beams on the lower framing wherever the lower framing meets the upper framing.
For your solution, you can remove on of the columns at the seating area [I'd choose the one on the bottom left of the seating area], since the beam would be able to span that distance. Similar with the lower roof framing at the seating area - too many columns. On the bottom and top E/W walls, try placing the column in the middle so that beam lengths are as close to equal as possible. Here was my solution, if it helps any -
viewtopic.php?f=8&t=2428#p6630Use Photoshop or MSPaint to resize images for posting.