Kyle was on alert since the incident with Randall, but nothing else happened. He didn't notice anyone following them, nor were there any suspicious activities.
After a week of constant vigilance amidst Kyle taking them around to sightsee, nothing happened. So much so that Kyle was beginning to think that Randall really did finally accept that he wasn't Dean.
So they spent the next week or so, just sightseeing the City. For Kyle, it was more like reliving his past life as he went through the familiar places. It was also a bit painful for him as he could 'see' the times he had gone there with his family.
Where did he take them, you might ask? Well, when in Country M, there was only one true thing to do besides going to the beach.
Eat.