TS, don't confuse East Coast Park (seaside park) with East Coast
Parkway (the expressway). Both are parallel and along the sea.
If you are coming from East Coast Park, follow the park all the
way to Fort Road Flyover. You can cycle under East Coast Parkway
here and cycle along Fort Road to...
Mountbatten Road...
Nicoll Highway (which is not an epressway despite the name.
Cycling on road is permitted and there are pavements too)...
[if cycling on pavement] Bras Basah Road... which becomes
Orchard Road...
[if cycling on road] Stamford Road... which becomes Penang
Road... which becomes Somerset Road... which is next to Orchard
Road.
(There are also many underpasses to cross under East Coast
Parkway.)