So you have $3000 (each) after flights?
I can only really speak for Tokyo, London and Paris (never been Stateside), but very rough costs would be something like:
Food: Depends on the time of year, but you can easily eat each day for around ¥2500 (~$25) if you stick to the cheapest places, around ¥5000 ($50) if you have a reasonably nice 'evening meal' and the sky's the limit if you want to eat well.
Hotel: The cheapest hotels can be as low as $50 a night for 2 if you search (so 5 nights = $250 for 2) though I'd budget more than that (say $100 a night) as a minimum if you travel peak, want to be more central or want breakfast included. Hotels.com is a great place to start.
Attractions: Disneyland is quite expensive (around $60 for a 1 day passport), and sumo (for a good seat) is around the same. The main car show is something like $30 to get in. Temples are usually free, as is Tsukiji fish market, gardens are usually ¥300-800 (around $8, say $30 total).
Transport: (Assuming you skip bullet trains and the like) local travel adds up, particularly down to Mt Fuji, so I'd budget around $20 a day for that, and maybe $20 contingency (total $120).
Total: For 5 days with some breathing room per person: meals $250, hotel $250, attractions $120, transport $120 = $740.
Food: Another world city, with everything from cheap takeaway food to 3 Michelin star restaurants. From my experience London has fewer 'low to mid-range' restaurants than Tokyo, and a lot more tourist traps, so I'd suggest a little more here, around $60 per day (though of course you can survive on sandwiches and fast food for much less than that - this assumes a decent evening meal with drinks at around $30 per head)
Hotel: All depends where in London you want to stay, but there are budget chains all over the place (Premier Inn, Travelodge) with decent, clean (but small) rooms available from $100 a night when on special offer. Again, to be on the safe side I'd set aside a little more, say $150 per room per night. So 4 nights = $600 ($300 each)
Attractions: The big commercial London attractions aren't cheap - the London Eye is around $30 - but most public museums and art galleries are free (except for special exhibitions). You can also get some combined tickets which offset the cost, and cheaper tickets if you buy online in advance. If you plan on doing a lot, you're probably looking at around $120 per person total for a mix of different attractions.
Transport: A 1 day Travelcard on the Underground is around $12. Alternatively you can get an Oyster card which you 'top up' with cash. On any given day, regardless of the number of journeys, you'll never be charged more than the equivalent 1 day travel card - so say $50 for 4 days.
Total: For 4 days with some breathing room per person: meals $240, hotel $300, attractions $120, transport $50 = $710.
Food: As with London and Tokyo, it all depends on how well you want to eat. Street stands, cheap pizza places and studenty-buffet all you can eat deals are all available, as is haute cuisine and more exotic fayre. When I last went we had coffee and croissants for breakfast (~$10), a sit down lunch set (~$20) and usually the 'fixed menu' dinner with some wine (~$30). It all depends on your definition of 'nice' however - good wine plus 3 a la carte courses could easily set you back $100+ per head.
Hotel: I last stayed in a private room in a hostel, which was around $20 per night. Hotels are like London - there are chains of budget hotels in lesser known districts with rooms from $70 per night, and there are the chains of luxury hotels for $400 per night. I'd budget $150 per room per night for a 3 star.
Attractions: Unfortunately many of Paris' museums and art galleries require a ticket (unlike the U.K.), as do most of the major attractions you mention. However, some churches and similar venues are free / donation only. Disneyland is ridiculously expensive at around $65. I'd say $150 inc. Disneyland is a good estimate.
Transport: Paris is a lovely city to walk around, and it's also a cheap way to see the sights - soaking up the atmosphere is part of the fun. Alternatively there are numerous passes, starting at around $13 for inner city, 1 day (zones 1-3) on the Metro / buses etc. Eurostar to Paris can be pricey, but booked in advance starts at around $70 1 way.
Total: For 3 days with some breathing room per person: meals $180, hotel $225, attractions $150, transport $100 = $675.
For these three then: $2125.
I imagine LA is comparable to the three cities above, however the big cost from your itinerary seems to be NYC at New Year. If it's anything like my home city (Edinburgh) the costs of everything skyrocket - hotels, food, drinks, the whole lot. Check this out thoroughly before you go.
Of course, there will be other expenses (souvenirs, bottled water or drinks, airport transfers, unexpected big nights out that just happen, and all manner of other costs) that are hard to accurately estimate. When I plan travel I usually include a hefty contingency fund.
In summary, I think $3000 is at the budget end of the spectrum, requiring a bit of booking, investigation and money savvy!
Hope this helps, and enjoy your travels!
Sources: personal experience, hotel booking sites, travel booking sites attraction sites