Is the location of the property suitable for you? Check transport connections, local facilities, schools, etc.
Does it offer the right accommodation? Do you have your furniture or are you looking for a home with everything supplied?
Does the accommodation seem secure? Look for potential nuisances: pubs, schools, noisy businesses in the area. Is the garden or close tidy and well maintained? Who maintains them and are there any extra costs? Does the property appear to be in good order internally and externally? Are there any repairs needing done? When do the bin men come?
Check the council tax banding - this can add substantially to your monthly expenditure.