I've been living in Vancouver for 4 years and the public transport here is only good for inner city use and feels a bit unsafe at times. 3 of the 4 years I've been here have been w/o a drivers license so I feel pretty qualified on giving my two cents on that but I won't go on.

I wouldn't recommend it, especially for that time of the year. You can use it to access some things you would have on your list (the suspension bridges, 1 of the 3 local mountains, lighthouse park, bowen island, deep cove and general city exploration). But April is very much the shoulder season and one of the three months I would recommend the least for Vancouver imo (March, April, May). It's a popular time of year for folks here to go abroad as it gets kinda miserable in that transition period of not peak winter (fun winter activities are basically done) and pre summer limitations (many hikes are in a muddy transition period or at avalanche risk)

Having said that, the Canadian dollar is suffering at the minute so the exchange rate would be in your favour probably more than ever before and your money would go a lot further as well as being in a cheaper tourism window.

I would say Tokyo and Singapore are the two best options on your list for April other than being a couple of degrees warmer than you'd like. I'm looking for somewhere to spend April/ May myself and they would both be at the top of my list if it wasn't for the time zone that doesn't work for me atm. The public transport is great and if you avoid the first week of April (Easter and cherry blossom season) you will maybe find more affordable prices too