Do you mean a Toddler Group? Playgroup to me means what we now call a Pre-School (typical children aged 2.5yrs-5yrs attending for either a morning or afternoon session without a parents staying with them).
Assuming you mean a toddler group - where parents stay with their children, then:
I would aim to setup the hall (or whatever venue it is) so that things are always in the same place as much as possible. That consistency can help children who are nervous of new places become accustomed to how things work at toddler group.
Have a variety of different things set up so that children can go between them - attention span of young children can be rather short.
Some things to have:
Playdough table - make your own playdough, it keeps a couple of weeks in a fridge. Have a variety of cutters and implements to make marks in the playdough.
Jigsaw table - a variety of jigsaws, the type where you lift pieces in/out tend to be easier, or ones which slot together in a base. Avoid thin cardboard jigsaws, chunky wood pieces are harder to lose. If you have quite a supply of jigsaws, rotate them on a weekly/bi-weekly basis such that the table has a couple from the previous week plus a couple of new ones.
Painting corner. Easels setup on some kind of washable matting. Washable paint is a must, if you can get it powerpaint I find is still the best as you can add washing up liquid to it which makes bubbles (children love bubbles) and helps it come out of clothing. Have a painting drying rack and a policy that any paintings left on the rack at the end of the session are put in recycling. Have a pencil available, so that names can be written on the paintings.
Wooden train - while it isn't as exciting as being able to build the track anyway they like, glueing the track to a board will help stop them throwing the track around, stop bridges constantly falling over etc.
Drawing table - chunky pencils, chunky crayons. Cover the entire table in paper, so that can be drawn on, plus provide some loose paper for drawing. Let the children experiment.
If you are doing a sing song time... don't make everyone take part. Some children just won't do that, have a singing group by all means but do expect some parents and children not to participate.
Consider how coffee/tea for adults is to be done. Some groups have the facility available all the time, whilst others restrict it to a specific 'snack' time. Consider the dangers involving hot drinks and young children, try to make sure parents have places to put cups/mugs out of reach of children.