This is how I would do it:
library(tidyverse)
set.seed(1)
df <- data_frame("x" = sample(x = 200:700, size = 10, replace = TRUE),
"y" = sample(x = 0:400, size = 10, replace = TRUE),
"z" = sample(x = 0:200, size = 10, replace = TRUE))
df
#> A tibble: 10 x 3
#> x y z
#> <int> <int> <int>
#> 1 523 84 109
#> 2 366 276 164
#> 3 328 361 33
#> 4 617 329 105
#> 5 670 262 125
#> 6 498 328 88
#> 7 469 78 171
#> 8 665 212 32
#> 9 386 36 83
#>10 506 104 162
df$z <- ifelse((df$x > 300 & df$x < 600) & (df$y > 0 & df$y < 100) & (df$z > 160), 115, df$z)
df
#> A tibble: 10 x 3
#> x y z
#> <int> <int> <dbl>
#> 1 523 84 109
#> 2 366 276 164
#> 3 328 361 33
#> 4 617 329 105
#> 5 670 262 125
#> 6 498 328 88
#> 7 469 78 115
#> 8 665 212 32
#> 9 386 36 83
#>10 506 104 162
#(#7 was updated to 115 as it met all the criteria)
Edit
As usual, @TIC's answer is better than mine (fewer steps -> faster) but not by much on my system with a million rows. The data.table method is quickest:
library(tidyverse)
set.seed(1)
df <- data_frame("x" = sample(x = 0:700, size = 1000000, replace = TRUE),
"y" = sample(x = 0:400, size = 1000000, replace = TRUE),
"z" = sample(x = 0:200, size = 1000000, replace = TRUE))
ifelse_func <- function(df){
df$z <- ifelse((df$x > 300 & df$x < 600) & (df$y > 0 & df$y < 100) & (df$z > 160), 115, df$z)
}
transform_func <- function(df){
transform(df, z = replace(z, 300 < x & x < 600 & 0 < y & y < 100 & z > 160, 115))
}
rowsums_func <- function(df){
df$z[!rowSums(!(df >list(300, 0, 160) & df < list(600, 100, Inf)))] <- 115
}
library(data.table)
dt_func <- function(df){
setDT(df)
df[x > 300 & x < 600 & y > 0 & y < 100 & z > 160, z := 115]
}
mbm <- microbenchmark::microbenchmark(ifelse_func(df), transform_func(df),
rowsums_func(df), dt_func(df))
autoplot(mbm)

Edit 2
> system.time(ifelse_func(df))
user system elapsed
0.064 0.020 0.085
> system.time(transform_func(df))
user system elapsed
0.060 0.009 0.069
> system.time(rowsums_func(df))
user system elapsed
0.090 0.021 0.110
> system.time(dt_func(df))
user system elapsed
0.036 0.003 0.039