People try to give you a false sense of security telling you there are police all over the stairs up to the cross and you are very safe during the day. This is not true Myself and another girl were together and walking in Broad Daylight (1:00-2:00pm) down the stairs from the cross when we were attacked by two guys. Normal looking young local guys. We screamed and screamed and screamed and no one came. We were not far from the top where supposedly the cop was suppose to be. We eventually found out he had left minutes before that happened. We fought and screamed and scared off the guys they took off down the stairs. When we went to find police there were none around. We got a group of guys to walk us down the stairs. we did not see ONE cop along the path. This is absolutely not safe to walk. Do not listen to what people say. I believe sometimes there are a few police there but you obviously cannot count on them. If you want to go to cross take tuk tuk or taxi UP AND DOWN.
There will be tour guides wandering the parque, but they will ask for money to take you up to the cross. The tourismo police escort tourists for free 10am/3pm each day. Or better yet, walk up there yourself. From the park, head up north on 4a ave norte, until you hit the end, make a right turn, for couple blocks, you'll see a nice residential area on your left, follow the gradual uphill walk, then you'll see an intersection, on your left is the way to the hill (signs). Follow the steep steps/walk the motor roads (i like the vehicle roads because it's less prone to mugging). During day time, I feel very safe walking there alone, with a flow of traffic, and very visual presence of police everywhere. It's an amazing sights to see Antigua and Volcan Aqua.
In general, Antigua Guatemala is much safer than the rest of Guatemala. There is tourist police patrolling in the town. You can usually walk in the town at night without any problems. However, don't go to Cerro de la Cruz alone. You'd better go with the tourist police that escorts tourists to the hill twice a day (10:00am in the morning and 3:00pm in the afternoon) free of charge. The tourist police can be found on 4a Ave at the northeast of the Central Park.
A danger spot to mention is the cross on a hill overlooking Antigua. Crosses are customarily erected on a highpoint above Latin cities. If you choose to visit such shrines, do so in the morning. Robbery and assault are greater and greater possibilities as the day wears on.
If you are planning to walk the ten minutes up the hill to Cerro de Cruz to take in the panaroma, register with the tourist police beforehand so you can be accompanied. There have been many reports of theft and should not be done independently.
The fascinating view offered by the cerrito is magnificent. Although there are armed guards it is not advisable to climb venture out in the hillside alone or at night.