I would neither recommend XLRI nor MICA for a digital marketing course. Instead, go for an online Ed-tech Institute called IIM Skills. 

It is among the top 3 Online ed-tech Institutes offering high-quality digital marketing courses. They offer a strong knowledge of the basics and help in a better understanding of concepts. The course is of great quality and once can enroll in the institute from wherever you want. It covers 40+ significant components of the Digital Marketing structure. 

Here are a few features pertaining to the course:

• 180 hours of comprehensive Digital Marketing training with live online interactive classrooms.
• There are 120+ hours of assignments and 60+ hours of live training 
• Online mode of training and flexibility to choose between weekday as well as l
• Flexibility related to time and days for the course.
• The mentors have a great experience as they have worked with some of the most important brands and corporate organizations.
• A free demo class before enrolling for the course regarding details

This course is inexpensive and will save you both money and time.

You should choose IIM Calcutta. It is better in terms of peer group, faculty profiles, ranking across the country and abroad, location, alumni base, and placements. You will get better opportunities at IIM Calcutta. 

As per the recent statistics, IIM Calcutta placements for the sales and marketing sector are pretty good. Almost 14% of students received placements in General Marketing and Marketing sector. The average CTC offered by the companies in this sector is INR 29 LPA. 

IIM Calcutta also has a better brand value compared to IIM Lucknow. In the long run, you can benefit a lot from that.