Check if two values within consecutive dates are identical

To get a logical column, you check wthr value if equal to row before using lag after grouping by place. I added arrange for date to make sure in chronological order.

library(dplyr)

df %>%
  arrange(date) %>%
  group_by(place) %>%
  mutate(same = wthr == lag(wthr, default = NA))

Edit: If you want to make sure dates are consecutive (1 day apart), you can include an ifelse to see if the difference is 1 between date and lag(date). If is not 1 day apart, it can be coded as NA.

Note: Also, make sure your date is a Date:

df$date <- as.Date(df$date)

df %>%
  arrange(date) %>%
  group_by(place) %>%
  mutate(same = ifelse(
    date - lag(date) == 1, 
    wthr == lag(wthr, default = NA),
    NA))

Output

   date       place wthr  same 
   <chr>      <chr> <chr> <lgl>
 1 2017-05-06 NY    sun   NA   
 2 2017-05-06 CA    cloud NA   
 3 2017-05-07 NY    sun   TRUE 
 4 2017-05-07 CA    rain  FALSE
 5 2017-05-08 NY    cloud FALSE
 6 2017-05-08 CA    rain  TRUE 
 7 2017-05-09 NY    cloud TRUE 
 8 2017-05-09 CA    NA    NA   
 9 2017-05-10 NY    cloud TRUE 
10 2017-05-10 CA    rain  NA