You are going to need to give us a bit more information about this “grotto”…
If “grotto” is an indoor shrine, perhaps, if it is outdoors, no (unless there is an approved chapel on the grounds)
If “your place” is a private residence (your house), then no. There are certain individuals (usually priests living in a regular house, or religious hermits acting under the obedience of the bishop) who have obtained permission from the bishop to reserve the Blessed Sacrament in their chapel. No one is allowed to keep the Blessed Sacrament without approval by the bishop.
Also, from what I understand (at least in our Archdiocese) in order for any chapel to be granted permission to reserve the Eucharist they must have regular Masses celebrated there (at least twice a month I believe). Not sure if the same stipulation is used in other dioceses.
If you mean simply reserving the Blessed Sacrament in a tabernacle, that is addressed above. If you are talking about having the Sacrament exposed in Perpetual Adoration in a grotto, this is an entirely different matter. Unless the grotto is part of a parish, and has a secure chapel (or, if it’s in a chapel), approval for this is not likely to be given. Typicially a priest must request permission, and take responsibility for the housing arrangements of the Eucharist. Lay people typically take the initiative in this effort, and organize into Adoration teams that will be responsible for keeping a watch on the Blessed Sacrament, then this group will approach the pastor and propose the instituation of Adoration in the parish – this usually must happen before the pastor will even consider going to the bishop for permission.
It would help if you could clarify exactly what your situation is…
+veritas+