I believe the completed crossword should look something like this:
Or, alternatively, in the spirit of this month's Topic Challenge:
What's happened here? Well, it turns out that in order to fit all of the words into their spaces, we have to...
...replace some two-letter units with their equivalent Japanese characters. Here I have chosen to use hiragana rather than katakana (if this is the wrong thing to do culturally speaking, I plead ignorance - I knew next to nothing about Asian alphabets before ending up deep into solving this puzzle...).
Note that in some instances (marked in red characters in the first diagram) the same symbol (or a variation on the same symbol) can be used to represent multiple different two-character units, e.g. the TI and DI in the very first box. In these instances I have chosen to portray the simpler of the two variations in the diagram.
As for the landmark represented in the crossword, I believe this is likely to be:
Tōkyō Sukaitsurī (a.k.a. 'Tokyo Skytree') - a neo-futurist building (hence the title) in the Japanese capital:
This does end in the 'RI' present in the grid in answer 2A. However, I must confess I am at somewhat of a loss as to what the numbers are intended to represent here, or why there are four grey boxes in the crossword grid indicating the vowels U, O, A, and E...
A full list of my clue answers is available here, with available grid space enumerated in square brackets:
Across:
2. Dormant Javanese volcano and abandoned nuclear power plant site (5) MURIA [3]
4. Walking with _________, first in a series of documentaries (9) DINOSAURS [6]
7. Mercury crater named after a 19th-century American novelist (9) HAWTHORNE [6]
10. Barry _________, loser of the 1964 US presidential election (9) GOLDWATER [7]
12. Indian alternative medicine system (8) AYURVEDA [6]
14. Soap opera that debuted on the same day as Channel 4 (9) BROOKSIDE [6]
16. Direct current generators using commutators (7) DYNAMOS [5]
18. ______ Hill, female Australian composer (6) MIRRIE [5]
20. White Star Line ship, later Gülcemal (8) GERMANIC [5]
22. "The better wow", per Urban Dictionary (5) WOWIE [3]
23. Small, often domesticated lizard (6) IGUANA [5]
24. Follower of Network or British (4) RAIL [3]
25. Squirrel's nest (4) DREY [3]
26. Nose pimple caused by excessive drinking (3-7) RUM-BLOSSOM [9]
27. Constellation containing the Spare Tyre Nebula (4) GRUS [3]
Down:
2. Pondered deeply (5) MUSED [3]
3. Touch by means of a mutual border (4) ABUT [3]
4. Yes album before The Yes Album (4,3,1,4) TIME AND A WORD [9]
5. Wood-cutter after the tree has been chopped down (5) SAWER [3]
6. Enyaq manufacturer (5) SKODA [3]
7. Pointed end of a hook, or a fish caught by it (4) BARB [3]
8. Anatomical homologue of the human ankle in a horse (4) HOCK [3]
9. Genus of duckbill eels (12) NETTENCHELYS [9]
11. Escher lithograph featuring a compound of three cubes (9) WATERFALL [8]
13. Saint Paul's role as author of Galatians, Romans and others (8) EPISTLER [7]
15. Component of an internal combustion engine pushing the intake/exhaust valve (6,3) ROCKER ARM [7]
17. viz. (6) NAMELY [5]
18. _______ Aouragh, Dutch anthropologist (7) MIRIYAM [5]
19. Genus of the black-winged kite (6) ELANUS [5]
21. South Korean League of Legends player currently playing for Rogue (7) MALRANG [5]