This is a very interesting card. You can't talk about this card without talking about this one here The Stars Are Right which gets shuffled into the encounter deck after it is played. Arkham Horror LCG now has various types of cancellation options to choose from within the game. It is almost getting to a point where I would restrict myself to the number of cancellation effects except when playing Diana Stanley. But, I wouldn't classify this as cancellation.
In all technical sense, this card doesn't "cancel" an effect. When it comes down to it though, you are not drawing an encounter card on the turn that this causes you to draw it's counter-point card The Stars Are Right.
Ward of Protection is the standard often referenced when discussions begin with cancellation effects. So, let's see what this does in comparison even though there are many others. By comparing these two cards we can see the differences and benefits of each.
Ward of Protection is actionless, whereas this card will cost you an action. Ward of Protection on the other hand costs you a resource and a sanity (offset often with other cards that protect you or help you with Agnes Baker, but it is still a cost) whereas Stargazing has no resource cost associated with it. In that sense, the action is somewhat offset by wards other costs. You also will get this action back later when you run across The Stars Are Right and gain a resource and card. So, you could argue that it is actually action efficient. It could be another investigator that decides to take these bonuses, so it has some flexibility there as well.
Ward is useful at almost any point in the game though, whereas this card is only useful when there is enough encounter cards left in the deck (you could get lucky of course and put it on top). So, you might draw this and find yourself not able to play it. In smaller player games such as solo, this could be the 10th card down for instance and there are only 9 turns left in the game. So your action would be wasted if you were to play it. In larger player games, if you see this early then great, you will likely see it being fruitful in your game. But in the larger player count, you also dig into the encounter deck and might find it unplayable for a couple turns mid to late game. So there are some dead-opportunities associated with this card in either situation. These cases that could happen are one of the draw-backs of this card.
It's icon is something that is nice to see here but ward also has this going for it.
Some might argue that you don't know what encounter card you would have drawn in its place with The Stars Are Right. This is where using the term 'cancel' associated with this card isn't appropriate. It is basically saying that in the future, you just don't draw an encounter card that phase and you will get your banked action you spent earlier back (or something will since it is targetable).
Ward of protection is there to keep you from that "Oh sheeet" moment. This doesn't protect you from the cards you know are in that deck waiting for you. It at best delays those cards one turn later into the game.
I think that this is a nice support card for mystics to slow the dangers that are ahead of you and I think I feel better about it in multiplayer scenarios rather than the solo play and just relying on lady luck.