Is it safe to walk around Paddington at night?
Paddington is also very safe. You and your family can safely walk to Paddington’s many restaurants, Hyde Park, and the Paddington Waterside. Either area is convenient for Heathrow. Paddington more so if you’re going by overground train; Kensington if you’re going by underground train via South Kensington station. I’d be happy to stay in either area; my slight preference would be for Paddington because it feels busier.
How not to dress like a tourist in London?
Dress like a local. Look, the iHeart London jumper you grabbed at Camden Market might be cute but it screams tourist. Londoners rarely wear workout clothes unless it adds you off to the gym. Just stick to jeans, T shirts, jumpers, and jackets and definitely layer up for the unpredictable weather. In London, wear black, black, and more black. To avoid looking too much like a tourist, bring a raincoat rather than a windbreaker.