Best time to buy currency? USD

Off to the states next week and still have to sort some dollars out

I was advised the post office is the most convenient and best value exchange
available with no commission.

I want to exchange about 1000 euro to usd in cash.

Does the exchange rate fluctuate much daily or will it matter at all whether I buy
my dollars tomorrow or the day before I go next week?

The exchange rate can vary by as much as 1-2c per day although if you are going next week there is unlikely to be any huge variation. If you want to get very scientific, there are historical rates and graphs on the ECB website which should give you the broad trend.

In your case, given the timescale and amount involved, you are talking a variation of a few euro at most...