From my own experience as a mum with a toddler, I would recommend the following:
The Toy Library
Sure Start North Moor Children's Centre in Kenton, has a free, relaxed and informal play session for under 5’s each Friday. All the toys can then be borrowed and taken home. The session is open 9:30am - 11am on Halewood Avenue, Kenton, (NE3 3RX).
Museums and Galleries
The Laing Art Gallery has an excellent under 5’s area where little ones can use the dress up box, play with blocks, work out simply puzzles, read books, press buttons. We’ve been using it regularly since my little one was 9 months old. It’s a lovely space, next to the café in the Laing, and free to everyone at anytime. http://www.twmuseums.org.uk/laing I would also recommend the play space in the National Glass Centre in Sunderland. After watching the glass blowing display in wonderment, we then took our toddler around the free permanent exhibition in the National Glass Centre. He especially enjoyed the magic mirrors and again, a good under 5’s area with blocks, toy cars and chalkboards. http://www.nationalglasscentre.com/home.html Monkwearmouth Museum has the best under 5’s area in my opinion. There’s a huge dress up box with transport related uniforms, a brightly coloured children’s train, trains sets and viewing deck where little ones can watch the metro passing by: http://www.twmuseums.org.uk/monkwearmouth.
All of these activities are free!