Ooh, that’s a tough one. The following advice comes with the caveat that there will always be exceptions to any rule (as you can see below, Derby by Carly & Art looks pretty comfortable outdoors). The key here, as with almost anything, is to carefully consider what risks are involved, mitigate those risks whenever possible, and carefully decide if those risks are outweighed by the benefits.
In most instances, your house rabbit probably shouldn't go outside for playtime. As a domesticated pet, your bunny has not had to learn the necessary skills to survive outside by itself. However, it still holds some very deeply ingrained habits and beliefs based on its DNA as a prey animal. You need to consider situations from the rabbit’s point of view. This requires you to “think like a rabbit,” and take some time to understand how the world looks to them.
There are many dangers for a bunny about in the world, whether you are in an urban area, a suburban subdivision, or a rural area. Cats, dogs, children, hawks, foxes, coyotes, raccoons, pesticides on lawns and gardens, poisonous plants… the list goes on and on. Even the shadow of an airplane passing overhead can be horribly frightening to a bunny. Remember, they are prey animals! A dark shadow coming over them could be a large bird swooping in to snatch them up. A frightened bunny can run amazingly fast (faster than you), squeeze through impossibly small holes in fences, into buildings, under decks, and jump and/or twist in such a way they break their own back.
As a result, what may sound like a relaxing afternoon outdoors to you may actually be a very stressful event for your rabbit.
Your yard may appear safe, but there are numerous dangers lurking just outside. Chances are, you cannot respond quickly enough to provide safety for your pet should these dangers come into play. Many hawks can dive at speeds over 200 miles per hour and can see prey from up to a mile away! I don’t think anyone could respond quickly enough to combat that. (And you'd be surprised how many urban areas have hawks.) Remember, as a prey animal bunnies think nearly everything is trying to do them harm. And often, they are right! An unfamiliar loud noise can cause a bun to bolt. They are quick to dart somewhere they feel may be safe, like the crawls pace under your home or beneath your deck. Trying to extract a determined and/or frightened bunny from there may be nearly impossible.
If you decide that your rabbit is comfortable and confident enough to enjoy time outside, do all you can to minimize the other risks out there. While a risk may be slim, it only takes ONCE for something tragic to happen. You can put them into a playpen, and it is recommended to have a cover on top to cut down on the risk of hawks and the fear of passing shadows. An x-pen with a fitted sheet stretched over the top works well.
Additionally, buns can dig very quickly through the ground and squeeze through small openings. If you do chose to take your rabbit outside, you should never leave them unattended. Provide continuous monitoring, even if they are in a playpen.
A better option is to use an enclosed porch or backyard aviary with a solid floor. Caution is still needed, as even then a curious dog or raccoon can be a cause for fright for your bunny, and may even burst through a screen to get to your rabbit.
It may be much easier to safely bring elements of the outside in to your bunny, be it the occasional pesticide free plant as a treat or by opening a screened window that is near their safe and secure indoor bunny home for fresh air.
As their caretaker, you have to make certain that if you are to allow them outside that no harm can come to them. As the above examples illustrate, that can be extremely difficult. It depends upon your particular situation and the local environment, but in most cases… I wouldn’t risk my bunny’s life on it. Your bun would enjoy just as much some focused playtime with you on the living room floor of their familiar home.