I have some fisher price roll arounds for dd, we have one knocking around that got given to us in a bunch of hand me downs for ds and she loves chasing after it and rolling about. Ds still likes it too and he will be 3 in Jan. Because both mine have Christmas/Jan birthday we try to get stuff to last the whole year ahead. When ds was 1 we got stuff like a rocking horse, toddle truck, ride on car, some of which he used right away and some of which he grew in to. All are still used and dd is fast growing into them.
DD got most use out of her V Tech walker at this age. I think they're about £35 but she played with it almost every day for over a year.
As for things to open - there wasn't really much dd needed or played with (and we have so much stuff off other people) so we just bought practical stocking filler type things (little toothbrush, cutlery set with favourite tv character on, bath toys, little books etc)