I wanted to try Lululemon since a friend used to work for them, but in Hong Kong they only stock small sizes, have mostly neutral colours and the sales staff are quite judgemental (Lululemon is usually in fancier, expensive malls, but still...)
Anyway, I've found that some of the more 'traditional' sports brands fit my hourglass shape well & stay put better (like Adidas, Reebok, Puma & Asics), as long as I avoid the 'Asian sizing' racks. Asics may be a Japanese brand, but their size large tops have good waist & shoulder shaping & don't pull on me when I'm in motion. Reebok have very comfortable leggings - their sports bras are very supportive but I think made for smaller builds & cup sizes, so that may work for you. Adidas also have tops with good shaping, comfortable bottoms that stay up, & elevated streetwear that looks appropriate for wearing outside of the gym (many people here have that sporty luxe style, so there's no surprise that we actually have a Adidas x Yohji Yamamoto store here lol - Adidas Stan Smiths are ubiquitous at work, & one of the graphic designers wears Kangol bucket hats & camo bomber jackets with panache, so you can imagine what the street style look is like out here). Puma have good fits if you size up enough, & their leggings offer good compression.
For me personally, Nike here does not work. Their shoes run small & narrow and their clothes are cut with a much smaller & less curvier figure in mind. If this sounds like your body though, then you may be in luck!
As for covering up to be outside, I usually bring a normal coat & boots in winter (if trainers won't be insulating enough), & a scarf or light tunic for the summer. It's amazing how well an outfit can transition if you keep colours & proportions in mind. If I'm wearing a yellow top, pink trainers & black leggings, I'll throw on a light, black, sleeveless dress over the top & orange/ sunset coloured scarf, & suddenly I don't look like I'm in gym gear anymore. This is also why I choose gym clothes that aren't too obnoxious with their branding, so that I can easily cover them up lol (no Adidas stripes running down the side of my legs or arms, for example). I also pick lightweight clothes that I can layer easily (like I said, bulky dolman sleeves aren't useful if I want to throw a coat over the top lol).
