Things I've bought for my nice and nephews nephews the last few years include a huge box of Playdough, a drumkit [though that was for four of them to share, heh], books [noisy ones are best of course], things that light up, magic painting books, any rubbish with their favourite characters on, slimy/squishy things like goop in a jar or sticky body parts, dart guns, a dartboard [er, a velcro one, that is], simple model planes/cars [like five or six pieces of card that slot together], threading cards/buttons, simple card games like Pairs, lots of pens/pencils/felt tips etc, balloons [they do light up ones, too], bubble wands, little games like Tiddlywinks, colour by numbers books, lots of various toy vehicles with different functions, educational [but fun!] posters...
I often find it difficult to find something that they would really enjoy [and use] for a reasonable price, so I tend to get them several smaller cheaper things that I know they'll actually like, and it's more fun in the unwrapping anyway. Having said all that, it depends on your relationship with your niece and nephew but I know for mine the best present is getting to go out with me. I've just recently taken the oldest two out with me to shop for what they wanted within a limit, and they loved that. Might be a bit of a pointless exercise for the three year old though [the choosing presents bit] as they tend to get so overwhelmed with choice they either want nothing or everything, but going out could still be an option maybe.