unni_110,If there is a will there always is a way! Of course going to park is an alternative but there always is a fear of getting caught either by authorities/ cops or by the people you both know! But if you can opt for hotel you can go to some tourist place near your place which would be few kilometers away so after enjoying a day over there you could be home by evening safely without being suspicious . At these place hotel owners are mostly money minded and do not insist on much .But ensure that the hotel you are going to is not a seedy one being used as on hour basis joint ,
It would be better if you opt for a up market good quality hotel rather than going to cheap guest houses or lodges near bus stands or railway stations.
And if you both are too young to be believed as a married couple then she can wear a ' mangalsutra' to deceive the unwanted suspicions. Here however i am presuming that you both are above age of 18 years old and so are adults and knowing what you have been doing, If that not being the case do not heed to this advice strictly.