Atoll sources are accreting neutron star (NS) low-mass X-ray binaries. We present a spectral analysis of four persistent atoll sources (GX 3+1, 4U 1702$-$429, 4U 0614+091, and 4U 1746$-$371) observed for $sim20$ ks each with NuSTAR to determine the extent of the inner accretion disk. These sources range from an apparent luminosity of $0.006-0.11$ of the Eddington limit (assuming the empirical limit of $3.8times10^{38}$ ergs s$^{-1}$). Broad Fe emission features shaped by Doppler and relativistic effects close to the NS were firmly detected in three of these sources. The position of the disk appears to be close to the innermost stable circular orbit (ISCO) in each case. For GX 3+1, we determine $R_{in}=1.8^{+0.2}_{-0.6} R_{mathrm{ISCO}}$ (90% confidence level) and an inclination of $27^{circ}-31^{circ}$. For 4U 1702$-$429, we find a $R_{in}=1.5_{-0.4}^{+1.6} R_{mathrm{ISCO}}$ and inclination of $53^{circ}-64^{circ}$. For 4U 0614+091, the disk has a position of $R_{in}=1.3_{-0.2}^{+5.4} R_{mathrm{ISCO}}$ and inclination of $50^{circ}-62^{circ}$. If the disk does not extend to the innermost stable circular orbit, we can place conservative limits on the magnetic field strength in these systems in the event that the disk is truncated at the Alfv{e}n radius. This provides the limit at the poles of $Bleq6.7times10^{8}$ G, $3.3times10^{8}$ G, and $14.5times10^{8}$ G for GX 3+1, 4U 1702$-$429, and 4U 0614+091, respectively. For 4U 1746$-$371, we argue that the most plausible explanation for the lack of reflection features is a combination of source geometry and strong Comptonization. We place these sources among the larger sample of NSs that have been observed with NuSTAR.
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