Not a pilot but was aircrew (Flight Test Engineer) for several years with an Aerospace Engineering background. Also have flown a lot commercially for work and personal travel and on top of that, being an AvGeek I often put a lot of research into where to sit when flying in to certain places.

For the flightpaths, yes there are a lot of variables beginning with weather at your origin and destination and en route. En route, major weather systems and the patterns for the jetstream that day play a big role in the routes pilots and operations try to plan for to get the best fuel burn rate while also avoiding any severe weather. Other factors include airspace management and restrictions since all aircraft can't fly the same route at the same altitude at the same time. When flying international, overflight rights become a factor and airlines may either voluntarily or involuntarily avoid flying over certain countries, impacting routing decisions. For example, when flying from Dallas to Hawaii, the most direct route (the Great Circle Route) goes over Mexico but a flight will often stay north of the US-Mexico border to avoid going into airspace and incurring the fees from flying through Mexican airspace. Other times it's involuntary. Many airlines cannot fly over Russia right now due. When I flew to/from Korea a few years ago, our routings took us over Japan to keep us well clear of Russian airspace, adding an additional hour or two of flight time over what the flight might normally otherwise take. For landing and takeoff, in addition to the winds/weather, other factors can dictate what you may see, such as deconfliction with other airports in the area. In NYC, you can often receive what may seem odd or illogical flight patterns but all have to do with managing the traffic for 3 very busy airports plus several other smaller airfields and aircraft in the area.

For DXB-LHR, I can't speak to Dubai since I've never flown into/out of Dubai but for landing in Heathrow, I've found the right side is the best side to be on as if you land to the west (coming in from the east), you'll pass over downtown London and get views of Tower Bridge, the London Eye, Big Ben, Buckingham Palace, etc. which will be on the right side of the aircraft. If you land to the east (coming in from the west), you may still get a good view of London coming in as you fly past London to then come back around and land at LHR. Heathrow can be a mixed bag as I've landed and taken off in both directions over my flights to/from/through Heathrow. On my most recent trip through LHR, we landed from the west and a few hours later when I flew out we took off to the west so in neither case did we fly over downtown London. On the flight in, we were on the left side of the aircraft (which I selected for our departure out of Toulouse) and since we landed coming in from the left, we had a great view of Windsor Castle.

For LHR-LAX, when landing at LAX, Disneyland is too far off to see and it's unlikely you'll fly far enough south to see it while coming into LAX since you'd be coming from the north / east coming from Europe. It's not even easy to spot Disneyland when landing at Orange County (SNA) which is much closer to Disneyland. But if you're on the right side of the aircraft, you'll see downtown LA, the San Gabriel Mountains, and the Hollywood sign (well, if you can see any of it through the LA smog ).