Given your budget is $70 per person, it does put a limit on the high end choices, so Tacubo is out of the question.
Look into Sushi Kutani (Ginza) for lunch. I can’t remember exactly how much but you might be able to get by with around or slightly above $70 per person (e.g. chirashi, or a nigiri combo). If you don’t get full you can go up the street and look for a cafe with cake sets to fill up (or whatever savory plates the cafes offer). Kutani can be booked on opentable quite easily. Quality easily blows away most places in SF Bay Area and better value. Ask for the English menu. They won’t serve the lunch offerings during dinner (which will run 16,000 yen for the full course).
Look also into yakiniku (Japanese style BBQ, like Korean BBQ but smaller portions, different cuts). Yakiniku Champion and there may be a more popular competitor Kintan available in the Ebisu and Daikanyama area. Some friends prefer Ushigoro but it’s more of a brand name and maybe a bit harder to book. Either places will blow away Gyu Kaku for sure. Check and see if they have set courses, and if not then maybe they are all a la carte. To lessen the blow, look for possible fillers on the menu. May end up running a bit over $80 per person possibly.
You can also do a bang bang at an area called Hobo Shinjuku Norengai (very close to Yoyogi station just north of Shibuya)
You will have to research the individual restaurants for their menus and whether they are non smoking or not. Outside this collective group of restaurants are other eateries, though mostly casual. The upside is that you will be dining with people getting off work, so a lot more atmospheric and you will see how the working class unwind (which can be really fun). The downsides will be rowdy and loud. Hopefully someone in your party will order a drink, not sure if that’s expected for some of these drinking places. Beer or hi ball is easy (none for you though).
There are also some restaurants on the top floor of high end department stores (Shinjuku’s Takashimaya at Times Square and Isetan come to mind), so those will be easier and you can take a look at their menus. You can also explore the lower level of Tokyo Station (you have to go into the lower level before you exit the subway) where the shops and restaurants are and there are tons of affordable and quite delicious options as well.
You can also download the ramen beast app and go to ramenbeast.com desktop version of the website to scout out interesting noodle spots (lunch and dinner). Focus on the places that have tables…Kiraku in Shibuya has tables on the second floor, old school place with a great soy sauce broth and shallots (get the bean sprouts wonton ramen, supposed to be their signature). Otherwise if it’s a popular place with counter seats only, your party may be broken up.
For Shodai, the tables I think are on the upper level, the ground level are counter seats only.