Unless you are in a hotel, there is not really anywhere to leave luggage. Unfortunately in these times there would not be anywhere to leave it, due to the type of things people leave in luggage.

Times Square in Causeway Bay has some men's shop that sell jumpers Rgds

First thing to do is to buy an Octopus card - you can use if for public transportation and even some shopping - food/coffee etc. To be honest, I do not like the TST area (Kowloon) crazy busy and a lot of store pimps trying to get you to buy, walk in i.e., Bespoke suits, electronics, watches/jewelry, "massage" etc., really annoys me so much that I wish to escape. If you're walking around that area they are endless in their numbers and relentless in their aggressiveness for getting you to buy...to the point where I have to be rude - which, as a world traveler and expat for over 17 years, I hate that I have to get to "rude"...so, now, when I go to HK, I avoid TST/Kowloon like the plague. I prefer HK island/central/SOHO area because it's a lot more chilled out with galleries (Hollywood street) the escalators areas, starting at Wellington, cafes, restaurants and so on. I just find the HK island areas so less congested and crazy - just more my thing as a hood for hanging out. I've stayed at a few of the Butterfly hotels - just google Butterfly hotel hong kong - great places, small boutique style, not cheap but also not crazy expensive like others. Most Butterfly's do not have food service but heck, you're in HK so food is easy to get and the beds in the Butterfly are soft, yes, I wrote and you read it - beds are soft! Take a ferry to one of the islands, so worth the trip. I've been to Lantau, amazing little place that has no cars. Lots to see and do in a day or for one night. Ferries (Central) are super easy, cheap and frequent.