you can go to guangzhou by train or bus. there are many trains from shenzhen to guangzhou. the fast trains are to Guangzhou east , which will take 1 hour. and each day has many trains. the price is higher than by bus. you can also go to guangzhou by bus. also many bus in different bus stations are available everyday. in geranal, the first train or bus is from 7:00 and the last is at 11:00pm.
in respect of Hongkong, you can go there by plane. but Guangzhou East to Kowloon.
it is hard to say where is the best place in guangzhou. it depends on different people. Guangzhou is a nice place for shopping, like beijing Road, the places near Tianhe sprots Center, Shangxiajiu etc.