Quick answer
For a direct drive from western Singapore to LEGOLAND Malaysia in Iskandar Puteri, Tuas and the Second Link are usually the natural route. LEGOLAND's directions also describe a route from Woodlands through Danga Bay and the coastal highway. Compare the two checkpoint approaches on your travel day.
Driving via Tuas
LEGOLAND's directions send drivers through the Tuas Second Link, then toward EXIT 312 in Malaysia. This often suits travellers starting in west Singapore. The checkpoint can still be busy, so check current Tuas images and any ICA advisory before departure.
Driving via Woodlands
Woodlands is also a possible route. LEGOLAND describes continuing through Johor Bahru toward Danga Bay and the coastal highway. It can suit an itinerary that includes central JB, but the city approach adds a different road segment. Compare the whole journey, not only the queue at the checkpoint.
Without a car
LEGOLAND's official directions list coach providers from Singapore. Check their current boarding points, departure times and ticket conditions directly; these can change by date. A cross-border bus to JB Sentral is a different journey and needs an onward transfer to reach the park.