Go to something like a meetup relevant to your interests, meet people, see where it leads.
For in-person interviews, suggest meeting outside of typical business hours-- grab an early morning coffee or after 6pm; even Saturday morning interviews are fine. You might be surprised just how flexible folks are.
I might add-- only pursue target opportunities you're seriously interested in. Don't waste anyone's time trying to get 'interview experience'.
Phone interviews can be tough - best to do well away from company out of respect if nothing else, but as suggested a lunch break is a good time for this and a park with maybe an ear piece or Bluetooth headset is recommended. And it may seem obvious, but don't actually eat or drink at any point while on the call...
For in person, again just from a moral stand point, these should be conducted on your own time but emphasize your desire to get as many possible done on that day. Don't try to overbook though - the worst thing you can do is miss our all for a reschedule at the last minute. But you can do so if they have a healthy buffer between, especially if one is an earlier round (ie. Phone screen after and day of in person has been doable for me, but you definitely should refuel at that point and try to take a breather.
You absolutely should be aware of the market opportunities and the relative value and respect that can factor in. It is your right, and I would say or obligation, to do so and insure both you and your employer are benefiting equally. All that being said, your current company shouldn't be paying for this pursuit, so be fair and do it on your own time. In business, being consistently courteous and reasonable in all your pursuits will genuinely help your cause and best position for you to receive the same.
BTW, I love going to work. :-)