A long stretch of time, like the summer holidays, can be daunting, but I suggest having a holiday routine.
First, find out what free or very cheap activities are happening at local museums, libraries, bookshops, sports centres, craft shops etc.
Then get a cheap notebook, pens and stickers - this will be your 4 year old's holiday scrapbook.
Make a rough timetable for the week. Get out in the morning and have quieter activities in the afternoon, such as filling in the scrapbook with pictures of what you've done that morning (look out for leaflets, tickets etc. that can be stuck in too.
Example
Monday mornings - Supermarket - you could make a scavenger hunt of things to spot as you go round - pack of stickers for good behaviour. Afternoon - baking.
Tuesday mornings - park - you could visit a different one each morning and rate them in different categories to find a winner. Picnic lunch. Afternoon - games
Wednesday mornings - library visit to read books and choose new ones for the week. Afternoon - singing and dancing at home.
Thursday mornings - woods/nature reserve/river walk etc. again, have a scavenger hunt of things to find. How many different small things can you find that can fit in a Smarties tube? You can put the smarties into a separate bag and reward each item found with a smartie. Afternoon - art.
Friday mornings - free museum. Afternoons - tidying up the house.
Of course this is just a suggestion, but can help to have a plan of action.