Scots will also be able to meet indoors with people from up to two other households from mid-July.
Hairdressers and barbers will also be allowed to re-open from 15 July, along with pubs and restaurants. It comes as the latest weekly figures for deaths in all settings show that the prevalence of the virus continues to fall in Scotland.
The Scottish Government has today published an update to its Route Map out of lockdown setting out further dates on easing restrictions.
"This greater clarity is possible because of the progress we have made against the virus - but delivering on the milestones depends on that progress continuing," Ms Sturgeon told MSPs at Holyrood today.
"I hope today’s statement will provide people and businesses with a bit more certainty now in their forward planning."
Today's Route Map sets out a series of indicative dates for the remainder of phase 2 and the early part of phase 3.
"It is our intention to lift the guidance advising people to travel no more than 5 miles for leisure and recreation purposes," Ms Sturgeon added.
Nursery and childcare services will be able to resume from 15 July, although capacity will remain restricted initially.
Self-contained holiday accommodation such as holiday cottages and lodges, or caravans where there are no shared services can open from 3 July, a fortnight before the rest of the tourism sector.
Beer gardens and other outdoor hospitality will be allowed to re-open on Monday 6 July.
Organised outdoor sports for children and young people can, subject to guidance, resume from 13 July.
Non essential shops within in shopping centres will re-open from 13 July, with other shops still allowed to open from Monday as planned.
Households will be able to meet people from more households outdoors from July 10.
And from July 10, Scots will be able to meet indoors with people from up to two other households, subject to physical distancing and strict hygiene measures, Ms Sturgeon said.
Museums, galleries, monuments, cinemas and libraries will also be able to reopen from July 15, but with precautions in place such as tickets being secured in advance - and subject to physical distancing and strict hygiene.
But theatres, bingo halls, nightclubs, casinos and other ‘live’ entertainment venues will not re-open any time soon.
Ms Sturgeon spoke out as the latest figures from National Records of Scotland (NRS) show a rise of 49 fatalities over the past week where Covid-19 was confirmed or suspected as the cause of death, taking the total to 4119. But this latest rise was down by 69 on the increase of 118 the previous week.
The First Minister said this showed the "real and sustained" progress which has been made in recent months.
But the two-metre social distancing rule remains in place in Scotland for the time being, although a review has ordered by Ms Sturgeon which will report at the start of next month.
It comes despite this restriction being reduced to one metre-plus south of the border.
"Our pace is slightly slower than England’s - but it is, in my view, right for our circumstances and, I hope, more likely to be sustainable than if we went faster," Ms Sturgeon said.
A decision on whether to make face coverings mandatory will be made after advice expected next week, with a campaign to promote and encourage their use to be launched.
Pubs, restaurants and cafes will also be be required to take names and contact details of customers and store these for four weeks when they reopen on July 15.
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